> restart;

> eqa1:=diff(y(x),x,x)+9*y(x)=sin(3*x);

eqa1 := (diff(y(x), `$`(x, 2)))+9*y(x) = sin(3*x)

> so1:=dsolve({eqa1,D(y)(0)=0,y(0)=1},y(x));

so1 := y(x) = 1/18*sin(3*x)+cos(3*x)-1/6*cos(3*x)*x

> eqa2:=diff(y(x),x,x)+10*y(x)=sin(3*x);

eqa2 := (diff(y(x), `$`(x, 2)))+10*y(x) = sin(3*x)

> so2:=dsolve({eqa2,D(y)(0)=0,y(0)=1},y(x));

so2 := y(x) = -3/10*sin(10^(1/2)*x)*10^(1/2)+cos(10^(1/2)*x)+sin(3*x)

> lso1:=rhs(so1);lso2:=rhs(so2);

lso1 := 1/18*sin(3*x)+cos(3*x)-1/6*cos(3*x)*x

lso2 := -3/10*sin(10^(1/2)*x)*10^(1/2)+cos(10^(1/2)*x)+sin(3*x)

> with(plots):

> plot({lso1,lso2},x=0..50,y=-10..10,color=[blue,red]);

[Plot]

>