微分方程作图
2012-05-17 11:39:52| 分类：
高等数学图形动画
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with(DEtools): 调用微分方程工具
with(plots): 调用绘图工具
de:=diff(y(x),x)=2*x*y(x); 定义微分方程
fxc:=DEplot(wffc,y(x),x=-2..2,y=-2..2): 画斜率场
jfq:=contourplot(y/exp(x^2),x=-2..2,y=-2..2): 画积分曲线
display(fxc,jfqx);
with(DEtools):with(plots):
wffc:=diff(y(x),x)=2*x*y(x):dsolve(wffc);
fangxiangcang:=DEplot(wffc,y(x),x=-2..2,y=-2..2,thickness=2):
jifenquxian:=contourplot(y/exp(x^2),x=-2..2,y=-2..2,contours=20,color=blue,thickness=2):
display(fangxiangcang,jifenquxian);
with(DEtools):with(plots):
wffc:=diff(y(x),x)=(cos(y(x))-y(x)*cos(x))/(x*sin(y(x))+sin(x)-1):
dsolve(wffc);fangxiangcang:=DEplot(wffc,y(x),x=0..4*Pi,y=0..4*Pi,thickness=2):
jifenquxian:=contourplot(y*sin(x)-x*cos(y)-y,x=0..4*Pi,y=0..4*Pi,contours=20,color=blue,thickness=2):
display(fangxiangcang,jifenquxian);
with(DEtools):with(plots):
wffc:=diff(y(x),x)=(cos(y(x))-y(x)*cos(x))/(x*sin(y(x))+sin(x)-1):
dsolve(wffc);fangxiangcang:=DEplot(wffc,y(x),x=-2..2,y=-2..2,thickness=2):
jifenquxian:=contourplot(y*sin(x)-x*cos(y)-y,x=-2..2,y=-2..2,contours=20,color=blue,thickness=2):
display(fangxiangcang,jifenquxian);
with(DEtools):with(plots):
wffc:=x*diff(y(x),x)+y(x)=sin(x):dsolve(wffc);
fangxiangcang:=DEplot(wffc,y(x),x=-2..2,y=-2..2,thickness=2):
jifenquxian:=contourplot(x*y+cos(x),x=-2..2,y=-2..2,contours=20,color=blue,thickness=2):
display(fangxiangcang,jifenquxian);
with(DEtools):with(plots):
wffc:=(x-y(x)^3)*diff(y(x),x)+y(x)=0:dsolve(wffc);
fangxiangcang:=DEplot(wffc,y(x),x=-2..2,y=-2..2,thickness=2):
jifenquxian:=contourplot(x*y-y^4/4,x=-2..2,y=-2..2,contours=20,color=blue,thickness=2):
display(fangxiangcang,jifenquxian);
with(DEtools):
DEplot((x-y(x)^3)*diff(y(x),x)+y(x)=0,y(x),x=-2..2,
y=-2..2,[[y(0)=1],[y(0)=0.3],[y(0)=1.5],[y(0)=-0.5],[y(0)=-1],[y(0)=-1.5]],linecolor=[blue,black,gold,navy,green,maroon],
color=violet,stepsize=0.01,scaling=constrained);
with(DEtools):with(plots):
wffc:=diff(y(x),x)=2*x*y(x):dsolve(wffc);
fangxiangcang:=DEplot(wffc,y(x),x=-2..2,y=-2..2,thickness=2):
jifenquxian:=contourplot(y/exp(x^2),x=-2..2,y=-2..2,contours=20,color=blue,thickness=2):
display(fangxiangcang,jifenquxian);
with(DEtools):
DEplot(diff(y(x),x)=2*x*y(x),y(x),x=-2..2,
[[y(0)=-1],[y(0)=-0.5],[y(0)=0],[y(0)=0.5],[y(0)=1],[y(0)=1.5]],
y=-4..4,linecolor=[gold,black,blue,red,brown,green],
color=grey,stepsize=0.01,scaling=constrained);
wffc:=3*x*y(x)^2*diff(y(x),x)=x^3+y(x)^3:dsolve(wffc,implicit);
fangxiangcang:=DEplot(wffc,y(x),x=-2..2,y=-2..2,thickness=2):
jifenquxian:=contourplot(x^2-2*y^3/x,x=-2..2,y=-2..2,contours=20,color=blue,thickness=2):
display(fangxiangcang,jifenquxian);
wffc:=diff(y(x),x$2)-diff(y(x),x)-2*y(x)=0:
tongjie:=dsolve(wffc,y(x)):
toplot:=[seq(seq(rhs(tongjie),_C1=-2..2),_C2=-2..2)]:
plot(toplot,x=-1..1,y=-10..10,thickness=3,color=red);
wffc:=diff(y(x),x$2)+2*diff(y(x),x)+y(x)=0:
tongjie:=dsolve(wffc,y(x)):tejie:=dsolve({wffc,y(0)=4,D(y)(0)=-2},y(x)):
tongjiequxian:=[seq(seq(rhs(tongjie),_C1=3..5),_C2=0..4)]:
p1:=plot(tongjiequxian,x=-2..2,y=0..8,thickness=1,color=red):
p2:=plot(rhs(tejie),x=-2..2,y=0..8,thickness=5,color=blue):
display(p1,p2,scaling=constrained);
wffc:=diff(y(x),x$2)+2*diff(y(x),x)+y(x)=0:
tongjie:=dsolve(wffc,y(x)):tejie:=dsolve({wffc,y(0)=4,D(y)(0)=-2},y(x)):
tongjiequxian:=[seq(seq(rhs(tongjie),_C1=2..6),_C2=0..8)]:
p1:=plot(tongjiequxian,x=-2..2,y=0..8,color=blue):
p2:=plot(rhs(tejie),x=-2..2,y=0..8,thickness=5,color=red):
display(p1,p2);
wffc:=diff(y(x),x$2)-4*diff(y(x),x)+13*y(x)=0:
tongjie:=dsolve(wffc,y(x)):
toplot:=[seq(seq(rhs(tongjie),_C1=-2..2),_C2=-2..2)]:
plot(toplot,x=-2..1.5,y=-20..20,thickness=3,color=red);
wffc:=diff(y(x),x$2)-4*diff(y(x),x)+13*y(x)=0:
tongjie:=dsolve(wffc,y(x)):
toplot:=[seq(seq(rhs(tongjie),_C1=-3..3),_C2=-3..3)]:
plot(toplot,x=-2..1,y=-20..20,thickness=2,color=blue);
wffc:=diff(y(x),x$2)+y(x)=2*x^2-3:
tongjie:=dsolve(wffc,y(x)):
toplot:=[seq(seq(rhs(tongjie),_C1=-3..3),_C2=-3..3)]:
plot(toplot,x=-2..2,y=-12..6,thickness=2,color=blue);
wffc:=diff(y(x),x$2)-2*diff(y(x),x)-3*y(x)=exp(-x):
tongjie:=dsolve(wffc,y(x)):
toplot:=[seq(seq(rhs(tongjie),_C1=-3..3),_C2=-3..3)]:
plot(toplot,x=-2..2,y=-12..12,color=blue,thickness=2);
wffc:=diff(y(x),x$2)-2*diff(y(x),x)+y(x)=(1+x)*exp(x):
tongjie:=dsolve(wffc,y(x)):
toplot:=[seq(seq(rhs(tongjie),_C1=-3..3),_C2=-3..3)]:
plot(toplot,x=-4..3,y=-10..10,color=blue);
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