用Maple解微分方程一阶微分方程

可分离变量方程

with(DEtools):

de:=diff(y(x),x)=2*x*y(x);

 dsolve(de, y(x));

DEplot(de,y(x),x=-2..2,y=-2..2,color=black,thickness=2);

 

 

 

 

with(DEtools):

de:= diff(y(x),x)=exp(2*x-y(x));

dsolve(de, y(x)); （通解）

dsolve({de,y(0)=0}, y(x)); （特解）

 

 

with(DEtools):

de:= (y(x)+1)^2*diff(y(x),x)+x^3=0;

dsolve(de,y(x));

 

下面给出隐式解（加一个：implicit）：

with(DEtools):

de:= (y(x)+1)^2*diff(y(x),x)+x^3=0;

dsolve(de,y(x),implicit);

 

 

 

齐次方程

 

 

with(DEtools):

de:=x^3+y(x)^3=3*x*y(x)^2*diff(y(x),x);

dsolve(de,y(x));

dsolve(de,y(x),implicit);

DEplot(de,y(x),x=-2..2,y=-2..2,color=red,thickness=2);

 

 

 

 

with(DEtools):

de:=(y(x)^2-3*x^2)*diff(y(x),x)+2*x*y(x)=0;

dsolve({de,y(0)=1},y(x));

dsolve({de,y(0)=1},y(x),implicit);

 

 

 

一阶线性方程

 

 

with(DEtools):

de:= diff(y(x),x)-2*y(x)/(x+1)=(x+1)^(5/2);

dsolve(de, y(x)); 

 

 

 

with(DEtools):

de:= diff(y(x),x)-y(x)*tan(x)=sec(x);

dsolve(de,y(x));

dsolve({de,y(0)=0},y(x));