用Maple解微分方程高阶微分方程

高阶微分方程

with(DEtools):

de:= diff(y(x),x$3)=exp(2*x)-cos(x);

dsolve(de,y(x)); 

 

 

with(DEtools):

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

dsolve(de,y(x));

dsolve({de,y(0)=1,D(y)(0)=3},y(x));

 

 

高阶线性微分方程

 

 

with(DEtools):

p:=-5:q:=6:

Q(x):=x*exp(2*x):

de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);

dsolve(de,y(x));

 

 

 

 

with(DEtools):

p:=0:q:=1:Q(x):=-sin(2*x):

de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);

dsolve(de,y(x));

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

 

 

 

 

  

 

with(DEtools):

p:=-10:q:=9:Q(x):=exp(2*x):

de:=diff(y(x),x$2)+p*diff(y(x),x)+q*y(x)=Q(x);

dsolve(de,y(x));

dsolve({de,y(0)=6/7,D(y)(0)=33/7},y(x));

 

 

 

 

 

欧拉方程

 

 

with(DEtools):

de:=x^3*diff(y(x),x$3)+x^2*diff(y(x),x$2)-4*x*diff(y(x),x)=3*x^2;

 

dsolve(de,y(x));