1. Nájdite všeobecné riešenie diferenciálnej rovnice y'-xy=2x
a partikulárne riešenie, ktoré vyhovuje začiatočnej podmienke
y(-2)=1. Nakreslite farebne sústavu integrálnych kriviek,
graf partikulárneho riešenia vyznačte hrubou čiernou čiarou.
Vypočítajte hodnotu partikulárneho riešenia y(1.25)=?

Clear All

All Clear

DSolve [ y ' [ x ] - x * y [ x ] 0 , y [ x ] , x ]

{ { y [ x ] x 2 2 C [ 1 ] } }

Clear[y]
DSolve[y'[x]-x*y[x]==2x,y[x],x]

{ { y [ x ] - 2 + x 2 2 C [ 1 ] } }

Clear[y]
DSolve[{y'[x]-x*y[x]==2x,y[-2]==1},y[x],x]//Simplify

{ { y [ x ] - 2 + 3 - 2 + x 2 2 } }


f[x_]=-2+c*Exp[x^2/2]
fp[x_]=-2+3*Exp[-2+x^2/2]
fp[1.25]

- 2 + c x 2 2

- 2 + 3 - 2 + x 2 2

- 1.1132016938678877

t = Table [ f [ x ] , { c , - 3 , 3 } ]

{ - 2 - 3 x 2 2 , - 2 - 2 x 2 2 , - 2 - x 2 2 , - 2 , - 2 + x 2 2 , - 2 + 2 x 2 2 , - 2 + 3 x 2 2 }

g1 = Plot [ Evaluate [ t ] , { x , - 3 , 3 } , PlotStyle { RGBColor [ 0.172549 , 0.635294 , 0.0156863 ] , RGBColor [ 0.0117647 , 0.309804 , 0.639216 ] , RGBColor [ 0.388235 , 0.0196078 , 0.627451 ] , RGBColor [ 0.023529 , 0.0470588 , 0.586275 ] , RGBColor [ 0.892157 , 0.809804 , 0.0235294 ] , RGBColor [ 1 , 0.0431373 , 0.0156863 ] } ]

[Graphics:HTMLFiles/cvicenie2L_1.gif]

Graphics

g2 = Plot [ fp [ x ] , { x , - 3 , 3 } , PlotStyle Thickness [ 0.005 ] ]

[Graphics:HTMLFiles/cvicenie2L_2.gif]

Graphics

Show[g1,g2]

[Graphics:HTMLFiles/cvicenie2L_3.gif]

Graphics


2. Nájdite všeobecné riešenie diferenciálnej rovnice (1+x)y'-x(1-y)=0
a partikulárne riešenie, ktoré vyhovuje začiatočnej podmienke
y(-1)=1. Nakreslite farebne sústavu integrálnych kriviek.

Clear All

DSolve[{(1+x)*y'[x]-x*(1-y[x])==0,y[-1]==1},y[x],x]//Simplify

DSolve :: bvnr : For some branches of the general solution, the given boundary conditions does not restrict the existing freedom in the general solution. More… "For some branches of the general solution, the given boundary conditions does not restrict the existing freedom in the general solution. \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, ButtonData:>\\\"DSolve::bvnr\\\"]\\)"

{ { y [ x ] - x ( x + ( 1 + x ) C [ 1 ] ) } }

Clear[y]

DSolve[(1 + x) * y '[x] - x * (1 - y[x]) 0, y[x], x]

{ { y [ x ] 1 + - x ( 1 + x ) C [ 1 ] } }

f [ x_ ] = 1 + c * ( 1 + x ) * Exp [ - x ]

1 + c - x ( 1 + x )

t = Table [ f [ x ] , { c , - 3 , 3 } ]

{ 1 - 3 - x ( 1 + x ) , 1 - 2 - x ( 1 + x ) , 1 - - x ( 1 + x ) , 1 , 1 + - x ( 1 + x ) , 1 + 2 - x ( 1 + x ) , 1 + 3 - x ( 1 + x ) }

g1 = Plot [ Evaluate [ t ] , { x , - 3 , 3 } , PlotStyle { RGBColor [ 0.172549 , 0.635294 , 0.0156863 ] , RGBColor [ 0.0117647 , 0.309804 , 0.639216 ] , RGBColor [ 0.388235 , 0.0196078 , 0.627451 ] , RGBColor [ 0.023529 , 0.0470588 , 0.586275 ] , RGBColor [ 0.892157 , 0.809804 , 0.0235294 ] , RGBColor [ 1 , 0.0431373 , 0.0156863 ] } ]

[Graphics:HTMLFiles/cvicenie2L_6.gif]

Graphics


3. Nájdite všeobecné riešenie diferenciálnej rovnice y'- 2*y/x = x^3 cos x
a partikulárne riešenie, ktoré vyhovuje začiatočným podmienkam
y(0)=0,y'(0)=0. Nakreslite farebne sústavu integrálnych kriviek,
graf partikulárneho riešenia vyznačte hrubou čiernou čiarou.

Clear All
DSolve[y'[x]-2*y[x]/x==x^3*Cos[x],y[x],x]//Simplify

All Clear

{ { y [ x ] x 2 ( C [ 1 ] + Cos [ x ] + x Sin [ x ] ) } }

Clear[y]
DSolve[{y'[x]-2*y[x]/x==x^3*Cos[x],y[-2]==2},y[x],x]//Simplify

{ { y [ x ] 1 2 x 2 ( 1 - 2 Cos [ 2 ] + 2 Cos [ x ] - 4 Sin [ 2 ] + 2 x Sin [ x ] ) } }

f[x_] = x^2 (c + Cos[x] + x Sin[x])

fp[x_] = 1/2 x^2 (1 - 2 Cos[2] + 2 Cos[x] - 4 Sin[2] + 2 x Sin[x])

x 2 ( c + Cos [ x ] + x Sin [ x ] )

1 2 x 2 ( 1 - 2 Cos [ 2 ] + 2 Cos [ x ] - 4 Sin [ 2 ] + 2 x Sin [ x ] )

t = Table [ f [ x ] , { c , - 3 , 3 } ]

{ x 2 ( - 3 + Cos [ x ] + x Sin [ x ] ) , x 2 ( - 2 + Cos [ x ] + x Sin [ x ] ) , x 2 ( - 1 + Cos [ x ] + x Sin [ x ] ) , x 2 ( Cos [ x ] + x Sin [ x ] ) , x 2 ( 1 + Cos [ x ] + x Sin [ x ] ) , x 2 ( 2 + Cos [ x ] + x Sin [ x ] ) , x 2 ( 3 + Cos [ x ] + x Sin [ x ] ) }

g1 = Plot [ Evaluate [ t ] , { x , - 9 , 9 } , PlotStyle { RGBColor [ 0.172549 , 0.635294 , 0.0156863 ] , RGBColor [ 0.0117647 , 0.309804 , 0.639216 ] , RGBColor [ 0.388235 , 0.0196078 , 0.627451 ] , RGBColor [ 0.023529 , 0.0470588 , 0.586275 ] , RGBColor [ 0.892157 , 0.809804 , 0.0235294 ] , RGBColor [ 1 , 0.0431373 , 0.0156863 ] } ]

[Graphics:HTMLFiles/cvicenie2L_9.gif]

Graphics

g2 = Plot [ fp [ x ] , { x , - 9 , 9 } , PlotStyle Thickness [ 0.005 ] ]

[Graphics:HTMLFiles/cvicenie2L_10.gif]

Graphics

Show [ g1 , g2 ]

[Graphics:HTMLFiles/cvicenie2L_11.gif]

Graphics


4. Nájdite všeobecné riešenie diferenciálnej rovnice y''-y'+y=cos x
a partikulárne riešenie, ktoré vyhovuje začiatočným podmienkam
y(0)=0,y'(0)=0. Nakreslite farebne sústavu integrálnych kriviek pre rôzne hodnoty konštánt.

Clear All

DSolve[y''[x]-y'[x]+y[x]==Cos[x],y[x],x]//Simplify

{ { y [ x ] x / 2 C [ 1 ] Cos [ 3 x 2 ] - Sin [ x ] + x / 2 C [ 2 ] Sin [ 3 x 2 ] } }

Clear[y]
DSolve[{y''[x]-y'[x]+y[x]==Cos[x],y[0]==0,y'[0]==0},y[x],x]//Simplify

{ { y [ x ] - Sin [ x ] + 2 x / 2 Sin [ 3 x 2 ] 3 } }


f[x_]= c1*Exp[x/2]*Cos[Sqrt[3]*x/2]-Sin[x]+c2*Exp[x/2]*Sin[Sqrt[3]*x/2]
fp[x_]=-Sin[x]+2*Exp[x/2]*Sin[Sqrt[3]*x/2]/Sqrt[3]

c1 x / 2 Cos [ 3 x 2 ] - Sin [ x ] + c2 x / 2 Sin [ 3 x 2 ]

- Sin [ x ] + 2 x / 2 Sin [ 3 x 2 ] 3

t1 = Table [ f [ x ] , { c1 , - 3 , 3 } , { c2 , 0 , 0 } ]

{ { - 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] } , { - 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] } , { - x / 2 Cos [ 3 x 2 ] - Sin [ x ] } , { - Sin [ x ] } , { x / 2 Cos [ 3 x 2 ] - Sin [ x ] } , { 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] } , { 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] } }

g1 = Plot [ Evaluate [ t1 ] , { x , - 9 , 9 } , PlotStyle { RGBColor [ 0.172549 , 0.635294 , 0.0156863 ] , RGBColor [ 0.0117647 , 0.309804 , 0.639216 ] , RGBColor [ 0.388235 , 0.0196078 , 0.627451 ] , RGBColor [ 0.023529 , 0.0470588 , 0.586275 ] , RGBColor [ 0.892157 , 0.809804 , 0.0235294 ] , RGBColor [ 1 , 0.0431373 , 0.0156863 ] } ]

[Graphics:HTMLFiles/cvicenie2L_12.gif]

Graphics

t2 = Table [ f [ x ] , { c1 , 0 , 0 } , { c2 , - 3 , 3 } ]

{ { - Sin [ x ] - 3 x / 2 Sin [ 3 x 2 ] , - Sin [ x ] - 2 x / 2 Sin [ 3 x 2 ] , - Sin [ x ] - x / 2 Sin [ 3 x 2 ] , - Sin [ x ] , - Sin [ x ] + x / 2 Sin [ 3 x 2 ] , - Sin [ x ] + 2 x / 2 Sin [ 3 x 2 ] , - Sin [ x ] + 3 x / 2 Sin [ 3 x 2 ] } }

g2 = Plot [ Evaluate [ t2 ] , { x , - 9 , 9 } , PlotStyle { RGBColor [ 0.172549 , 0.635294 , 0.0156863 ] , RGBColor [ 0.0117647 , 0.309804 , 0.639216 ] , RGBColor [ 0.388235 , 0.0196078 , 0.627451 ] , RGBColor [ 0.023529 , 0.0470588 , 0.586275 ] , RGBColor [ 0.892157 , 0.809804 , 0.0235294 ] , RGBColor [ 1 , 0.0431373 , 0.0156863 ] } ]

[Graphics:HTMLFiles/cvicenie2L_13.gif]

Graphics

t3 = Table [ f [ x ] , { c1 , - 3 , 3 } , { c2 , - 3 , 3 } ]

{ { - 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] - 3 x / 2 Sin [ 3 x 2 ] , - 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] - 2 x / 2 Sin [ 3 x 2 ] , - 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] - x / 2 Sin [ 3 x 2 ] , - 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] , - 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] + x / 2 Sin [ 3 x 2 ] , - 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] + 2 x / 2 Sin [ 3 x 2 ] , - 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] + 3 x / 2 Sin [ 3 x 2 ] } , { - 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] - 3 x / 2 Sin [ 3 x 2 ] , - 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] - 2 x / 2 Sin [ 3 x 2 ] , - 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] - x / 2 Sin [ 3 x 2 ] , - 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] , - 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] + x / 2 Sin [ 3 x 2 ] , - 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] + 2 x / 2 Sin [ 3 x 2 ] , - 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] + 3 x / 2 Sin [ 3 x 2 ] } , { - x / 2 Cos [ 3 x 2 ] - Sin [ x ] - 3 x / 2 Sin [ 3 x 2 ] , - x / 2 Cos [ 3 x 2 ] - Sin [ x ] - 2 x / 2 Sin [ 3 x 2 ] , - x / 2 Cos [ 3 x 2 ] - Sin [ x ] - x / 2 Sin [ 3 x 2 ] , - x / 2 Cos [ 3 x 2 ] - Sin [ x ] , - x / 2 Cos [ 3 x 2 ] - Sin [ x ] + x / 2 Sin [ 3 x 2 ] , - x / 2 Cos [ 3 x 2 ] - Sin [ x ] + 2 x / 2 Sin [ 3 x 2 ] , - x / 2 Cos [ 3 x 2 ] - Sin [ x ] + 3 x / 2 Sin [ 3 x 2 ] } , { - Sin [ x ] - 3 x / 2 Sin [ 3 x 2 ] , - Sin [ x ] - 2 x / 2 Sin [ 3 x 2 ] , - Sin [ x ] - x / 2 Sin [ 3 x 2 ] , - Sin [ x ] , - Sin [ x ] + x / 2 Sin [ 3 x 2 ] , - Sin [ x ] + 2 x / 2 Sin [ 3 x 2 ] , - Sin [ x ] + 3 x / 2 Sin [ 3 x 2 ] } , { x / 2 Cos [ 3 x 2 ] - Sin [ x ] - 3 x / 2 Sin [ 3 x 2 ] , x / 2 Cos [ 3 x 2 ] - Sin [ x ] - 2 x / 2 Sin [ 3 x 2 ] , x / 2 Cos [ 3 x 2 ] - Sin [ x ] - x / 2 Sin [ 3 x 2 ] , x / 2 Cos [ 3 x 2 ] - Sin [ x ] , x / 2 Cos [ 3 x 2 ] - Sin [ x ] + x / 2 Sin [ 3 x 2 ] , x / 2 Cos [ 3 x 2 ] - Sin [ x ] + 2 x / 2 Sin [ 3 x 2 ] , x / 2 Cos [ 3 x 2 ] - Sin [ x ] + 3 x / 2 Sin [ 3 x 2 ] } , { 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] - 3 x / 2 Sin [ 3 x 2 ] , 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] - 2 x / 2 Sin [ 3 x 2 ] , 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] - x / 2 Sin [ 3 x 2 ] , 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] , 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] + x / 2 Sin [ 3 x 2 ] , 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] + 2 x / 2 Sin [ 3 x 2 ] , 2 x / 2 Cos [ 3 x 2 ] - Sin [ x ] + 3 x / 2 Sin [ 3 x 2 ] } , { 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] - 3 x / 2 Sin [ 3 x 2 ] , 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] - 2 x / 2 Sin [ 3 x 2 ] , 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] - x / 2 Sin [ 3 x 2 ] , 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] , 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] + x / 2 Sin [ 3 x 2 ] , 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] + 2 x / 2 Sin [ 3 x 2 ] , 3 x / 2 Cos [ 3 x 2 ] - Sin [ x ] + 3 x / 2 Sin [ 3 x 2 ] } }

g3 = Plot [ Evaluate [ t3 ] , { x , - 9 , 9 } , PlotStyle { RGBColor [ 0.172549 , 0.635294 , 0.0156863 ] , RGBColor [ 0.0117647 , 0.309804 , 0.639216 ] , RGBColor [ 0.388235 , 0.0196078 , 0.627451 ] , RGBColor [ 0.023529 , 0.0470588 , 0.586275 ] , RGBColor [ 0.892157 , 0.809804 , 0.0235294 ] , RGBColor [ 1 , 0.0431373 , 0.0156863 ] } ]

[Graphics:HTMLFiles/cvicenie2L_14.gif]

Graphics

5. Nájdite všeobecné riešenie diferenciálnej rovnice y''+2y'+y=x e^(- x)
a partikulárne riešenie, ktoré vyhovuje začiatočným podmienkam y(1)=0, y'(1)=2.
Nakreslite farebne sústavu integrálnych kriviek pre rôzne hodnoty parametrov,
graf partikulárneho riešenia vyznačte hrubou čiernou farbou.

Clear All

DSolve[y''[x] + 2y '[x] + y[x] x * Exp[-x], y[x], x]//Simplify

All Clear

{ { y [ x ] 1 6 - x ( x 3 + 6 C [ 1 ] + 6 x C [ 2 ] ) } }

Clear[y]

DSolve[{y''[x] + 2y '[x] + y[x] x * Exp[-x], y[1] 0, y '[1] 2}, y[x], x]//Simplify

{ { y [ x ] 1 6 - x ( - 1 + x ) ( - 2 + 12 + x + x 2 ) } }

f[x_] = Exp[-x] * (x^3 + 6 * c1 + 6 * x * c2)/6

fp[x_] = Exp[-x] * (x - 1) * (x^2 + x + 12 * E - 2)/6

1 6 - x ( 6 c1 + 6 c2 x + x 3 )

1 6 - x ( - 1 + x ) ( - 2 + 12 + x + x 2 )

t1 = Table [ f [ x ] , { c1 , - 3 , 3 } , { c2 , 0 , 0 } ]

{ { 1 6 - x ( - 18 + x 3 ) } , { 1 6 - x ( - 12 + x 3 ) } , { 1 6 - x ( - 6 + x 3 ) } , { 1 6 - x x 3 } , { 1 6 - x ( 6 + x 3 ) } , { 1 6 - x ( 12 + x 3 ) } , { 1 6 - x ( 18 + x 3 ) } }

g1 = Plot [ Evaluate [ t1 ] , { x , - 3 , 3 } , PlotStyle { RGBColor [ 0.172549 , 0.635294 , 0.0156863 ] , RGBColor [ 0.0117647 , 0.309804 , 0.639216 ] , RGBColor [ 0.388235 , 0.0196078 , 0.627451 ] , RGBColor [ 0.023529 , 0.0470588 , 0.586275 ] , RGBColor [ 0.892157 , 0.809804 , 0.0235294 ] , RGBColor [ 1 , 0.0431373 , 0.0156863 ] } ]

[Graphics:HTMLFiles/cvicenie2L_21.gif]

Graphics

t2 = Table [ f [ x ] , { c1 , 0 , 0 } , { c2 , - 3 , 3 } ]

{ { 1 6 - x ( - 18 x + x 3 ) , 1 6 - x ( - 12 x + x 3 ) , 1 6 - x ( - 6 x + x 3 ) , 1 6 - x x 3 , 1 6 - x ( 6 x + x 3 ) , 1 6 - x ( 12 x + x 3 ) , 1 6 - x ( 18 x + x 3 ) } }

g2 = Plot [ Evaluate [ t2 ] , { x , - 3 , 3 } , PlotRange { - 10 , 15 } , PlotStyle { RGBColor [ 0.172549 , 0.635294 , 0.0156863 ] , RGBColor [ 0.0117647 , 0.309804 , 0.639216 ] , RGBColor [ 0.388235 , 0.0196078 , 0.627451 ] , RGBColor [ 0.023529 , 0.0470588 , 0.586275 ] , RGBColor [ 0.892157 , 0.809804 , 0.0235294 ] , RGBColor [ 1 , 0.0431373 , 0.0156863 ] } ]

[Graphics:HTMLFiles/cvicenie2L_22.gif]

Graphics

t3 = Table [ f [ x ] , { c1 , - 3 , 3 } , { c2 , - 3 , 3 } ]

{ { 1 6 - x ( - 18 - 18 x + x 3 ) , 1 6 - x ( - 18 - 12 x + x 3 ) , 1 6 - x ( - 18 - 6 x + x 3 ) , 1 6 - x ( - 18 + x 3 ) , 1 6 - x ( - 18 + 6 x + x 3 ) , 1 6 - x ( - 18 + 12 x + x 3 ) , 1 6 - x ( - 18 + 18 x + x 3 ) } , { 1 6 - x ( - 12 - 18 x + x 3 ) , 1 6 - x ( - 12 - 12 x + x 3 ) , 1 6 - x ( - 12 - 6 x + x 3 ) , 1 6 - x ( - 12 + x 3 ) , 1 6 - x ( - 12 + 6 x + x 3 ) , 1 6 - x ( - 12 + 12 x + x 3 ) , 1 6 - x ( - 12 + 18 x + x 3 ) } , { 1 6 - x ( - 6 - 18 x + x 3 ) , 1 6 - x ( - 6 - 12 x + x 3 ) , 1 6 - x ( - 6 - 6 x + x 3 ) , 1 6 - x ( - 6 + x 3 ) , 1 6 - x ( - 6 + 6 x + x 3 ) , 1 6 - x ( - 6 + 12 x + x 3 ) , 1 6 - x ( - 6 + 18 x + x 3 ) } , { 1 6 - x ( - 18 x + x 3 ) , 1 6 - x ( - 12 x + x 3 ) , 1 6 - x ( - 6 x + x 3 ) , 1 6 - x x 3 , 1 6 - x ( 6 x + x 3 ) , 1 6 - x ( 12 x + x 3 ) , 1 6 - x ( 18 x + x 3 ) } , { 1 6 - x ( 6 - 18 x + x 3 ) , 1 6 - x ( 6 - 12 x + x 3 ) , 1 6 - x ( 6 - 6 x + x 3 ) , 1 6 - x ( 6 + x 3 ) , 1 6 - x ( 6 + 6 x + x 3 ) , 1 6 - x ( 6 + 12 x + x 3 ) , 1 6 - x ( 6 + 18 x + x 3 ) } , { 1 6 - x ( 12 - 18 x + x 3 ) , 1 6 - x ( 12 - 12 x + x 3 ) , 1 6 - x ( 12 - 6 x + x 3 ) , 1 6 - x ( 12 + x 3 ) , 1 6 - x ( 12 + 6 x + x 3 ) , 1 6 - x ( 12 + 12 x + x 3 ) , 1 6 - x ( 12 + 18 x + x 3 ) } , { 1 6 - x ( 18 - 18 x + x 3 ) , 1 6 - x ( 18 - 12 x + x 3 ) , 1 6 - x ( 18 - 6 x + x 3 ) , 1 6 - x ( 18 + x 3 ) , 1 6 - x ( 18 + 6 x + x 3 ) , 1 6 - x ( 18 + 12 x + x 3 ) , 1 6 - x ( 18 + 18 x + x 3 ) } }

g3 = Plot [ Evaluate [ t3 ] , { x , - 3 , 3 } , PlotRange { - 10 , 20 } , PlotStyle { RGBColor [ 0.172549 , 0.635294 , 0.0156863 ] , RGBColor [ 0.0117647 , 0.309804 , 0.639216 ] , RGBColor [ 0.388235 , 0.0196078 , 0.627451 ] , RGBColor [ 0.023529 , 0.0470588 , 0.586275 ] , RGBColor [ 0.892157 , 0.809804 , 0.0235294 ] , RGBColor [ 1 , 0.0431373 , 0.0156863 ] } ]

[Graphics:HTMLFiles/cvicenie2L_23.gif]

Graphics

g4 = Plot [ fp [ x ] , { x , - 3 , 3 } , PlotStyle Thickness [ 0.005 ] ]

[Graphics:HTMLFiles/cvicenie2L_24.gif]

Graphics

Show [ g3 , g4 ]

[Graphics:HTMLFiles/cvicenie2L_25.gif]


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