Integrating factor method

Question

I'm confused with this particular question, so could someone please explain how to go about doing a question such as this one?

I want to place the following equation in a form suitable for using the integrating factor method: $$(x-3)\frac{dy}{dx}-y=(x-3)^2$$

I want to solve the above differential equation given $y=10$ when $x=5$.

Answer 1

for the particular solution make the ansatz $$y_p(x)=ax^2+bx+c$$ with $a,b,c$ real numbers. the solution is given by $$y=x(x-3)+C(x-3)$$