Example 3: Find a particular solution of .

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

> diff(exp(2*x)*(a*x+b),x,x)+exp(2*x)*(a*x+b)-exp(2*x)*x;

> p:=unapply(%,x);

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

Hence .