Transcript y(x)= −x C[1] Direzione del campo indotto

DSolve@y '@xD Š -y@xD, y, xD;
f@x_D = y@xD •. %@@1DD;
Print@D;
Print@Style@"yHxL=" f@xD, Bold, Red, 24DD;
Print@D;
g1 = Plot@
Evaluate@f@xD •. 88C@1D ® 0.1<, 8C@1D ® 1<, 8C@1D ® 4<<D,
8x, 0, 2.2<, AxesOrigin ® 80, 0<,
PlotRange ® 8-0.1, 2.1<, AspectRatio ® 1,
AxesLabel ® 8"x", "y"<,
BaseStyle ® 8FontSize ® [email protected]<,
PlotStyle ® 88RGBColor@0, 0, 0D, [email protected]<,
8RGBColor@0, 0, 0D, [email protected]<,
8RGBColor@0, 0, 0D, [email protected]<<D;
pt0 = Table@8x, y<, 8x, 0, 2, 0.25<, 8y, 0, 2, 0.25<D;
l0 = ListPlot@pt0,
PlotStyle -> Directive@Red, [email protected];
d = 0.1;
l1 = Graphics@8RGBColor@0, 0.5, 0.9D,
[email protected], Table@[email protected],
Line@88x, y<, 8x + 0.1, y - 0.1 * y<<D<,
8x, 0, 2, 0.25<, 8y, 0, 2, 0.25<D<, AspectRatio ® 1D;
Print@Style@"
Direzione del campo indotto ",
Bold, Blue, 24DD;
Show@8g1, l0, l1<, Frame ® TrueD
yHxL= ã-x C@1D
Direzione del campo indotto
2
SLIDE7_VISUALIZZAZIONE_CAMPO_INDOTTO_CL.nb
2.0
1.5
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SLIDE7_VISUALIZZAZIONE_CAMPO_INDOTTO_CL.nb
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DSolve@y '@xD Š -y@xD, y, xD;
f@x_D = y@xD •. %@@1DD;
Print@Style@"yHxL=" f@xD, Bold, Red, 24DD;
Print@D;
g0 = Plot@
Evaluate@f@xD •. 88C@1D ® 1<, 8C@1D ® 0.2<, 8C@1D ® 4<<D,
8x, 0, 2<, AxesOrigin ® 80, 0<,
AspectRatio ® 1, PlotRange ® 8-0.1, 2.1<,
AxesLabel ® 8"x", "y"<,
BaseStyle ® 8FontSize ® [email protected]<,
PlotStyle ® 88RGBColor@0, 0, 0D, [email protected]<,
8RGBColor@0, 0, 0D, [email protected]<,
8RGBColor@0, 0, 0D, [email protected]<<,
DisplayFunction ® IdentityD;
g1 = [email protected], 8x, 0, 2<, PlotStyle ®
8Red, [email protected]<D;
g2 = Plot@1, 8x, 0, 2<, PlotStyle ® 8Red, [email protected]<D;
g3 = Plot@2, 8x, 0, 2<, PlotStyle ® 8Red, [email protected]<D;
l0 =
Graphics@8Table@Line@88x, 0.5<, 8x + 0.3, 0.5 * H1 - 0.3L<<D,
8x, 0, 2, 0.1<D<, AspectRatio ® 1D;
l1 = Graphics@8Table@Line@88x, 1<, 8x + 0.2, 1 - 0.2<<D,
8x, 0, 2, 0.1<D<, AspectRatio ® 1D;
l2 = Graphics@8Table@Line@88x, 2<, 8x + 0.1, 2 H1 - 0.1L<<D,
8x, 0, 2, 0.1<D<, AspectRatio ® 1D;
Print@Style@"
Curve di livello
",
Bold, Blue, 24DD;
Show@8g0, g1, g2, g3, l0, l1, l2<,
DisplayFunction ® $DisplayFunctionD
yHxL= ã-x C@1D
Curve di livello
4
SLIDE7_VISUALIZZAZIONE_CAMPO_INDOTTO_CL.nb
y
2.0
1.5
1.0
0.5
0.5
1.0
1.5
2.0
x