# Math Help - First order DE problem

1. ## First order DE problem

For any of the constant value k, the function y is a solution of the last equation.

Find p and q.

I've tried subbing in y and y' but I need P and Q explicitly. Don't know what to do.

2. Anyone?

3. Originally Posted by DCU
For any of the constant value k, the function y is a solution of the last equation.

Find p and q.

I've tried subbing in y and y' but I need P and Q explicitly. Don't know what to do.

The key is the hint they gave you. It is true for every value of k

So you get
$\cos(x)-\frac{k}{x^2}+P(x)\left(\sin(x)+\frac{k}{x} \right)=Q(x)$

This is true for every value of k so pick some easy ones like
$k=0,k=1$ and solve for P and Q.