Example 4: Find a particular solution of .

Solution: Since a linear combination of and is of the form we have

> diff(a*cos(x)+b*sin(x),x,x)+a*cos(x)+b*sin(x)-cos(x);

> p:=unapply(%,x);

> solve({p(0)=0,p(1)=0,p(2)=0},{a,b});

No solution. Next, we ont color=#000000>No solution. Next, we try a particular solution of the form .

> diff(x*(a*cos(x)+b*sin(x)),x,x)+x*(a*cos(x)+b*sin(x))-cos(x);

> p:=unapply(%,x);

> solve({p(0)=0,p(1)=0,p(2)=0},{a,b});

Hence a particular solution is .