Maple dsolve(eq,var,options), eq , var , options . , , : type=exact. diff, , y'' + y = x : diff(y(x),x$2)+y(x)=x.
, . Maple , , _ 1, _ 2, ..
, , . , . , ( ), ( ).
dsolve . , (, ) rhs(%).
, y '+ y cos x =sin x cos x.
> restart;
> de:=diff(y(x),x)+y(x)*cos(x)=sin(x)*cos(x);
de: = 
> dsolve(de,y(x));
1
, 
1.
: Maple _ 1.
y ''-2 y '+ y =sin x + e - x.
> restart;
> deq:=diff(y(x),x$2)-2*diff(y(x),x)+y(x)=sin(x)+exp(-x);
deq:= 
> dsolve(deq,y(x));
: , , Maple _ 1 _ 2. , .
y ''+ k 2 y =sin(qx) : q ¹ k q = k ().
>restart; de:=diff(y(x),x$2)+k^2*y(x)=sin(q*x);
>dsolve(de,y(x));
. dsolve q = k.
>q:=k: dsolve(de,y(x));
: , , .
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dsolve ( ) . dsolve output=basis.
: y (4)+2 y ''+ y =0.
> de:=diff(y(x),x$4)+2*diff(y(x),x$2)+y(x)=0;
de: = 
> dsolve(de, y(x), output=basis);
dsolve , . 
, , y''(0)=2 
, y '(1)=0: 
. , n - 
.
1. : y (4)+ y ''=2cos x, y (0)=-2, y '(0)=1, y ''(0)=0, y '''(0)=0.
> de:=diff(y(x),x$4)+diff(y(x),x$2)=2*cos(x);
> cond:=y(0)=-2, D(y)(0)=1, (D@@2)(y)(0)=0, (D@@3)(y)(0)=0;
cond:= y(0)=-2, D(y)(0)=1, (D(2))(y)(0)=0, (D(3))(y)(0)=0
> dsolve({de,cond},y(x));
y(x)=-2cos(x)- x sin(x)+
2. : 
, 
, 
. .
> restart; de:=diff(y(x),x$2)+y(x)=2*x-Pi;
de: = 
> cond:=y(0)=0,y(Pi/2)=0;
> dsolve({de,cond},y(x));
y(x)=2 x -p+pcos(x)
: .
> y1:=rhs(%):plot(y1,x=-10..20,thickness=2);
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