> diffeq:=diff(y(x),x$2)+omega^2*y(x)=0;
inits:=y(0)=1,D(y)(0)=-2;

> sol:=dsolve({diffeq,inits},y(x));

> deriv:=diff(rhs(sol),omega);

> approx:=y(x)=0.15*subs(omega=2,deriv)+subs(omega=2,rhs(sol));

> actual:=y(x)=subs(omega=2.15,rhs(sol));

> with(plots):

> plot([rhs(actual),rhs(approx)],x=0..5*Pi,y=-5..5);

>

>

>