# Integrating factor method

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 $x=5$.

• can you use $\LaTeX$ please? – Dr. Sonnhard Graubner Oct 5 '16 at 10:49
• is it $$\frac{dy}{dx}-y=(x-3)^2$$? – Dr. Sonnhard Graubner Oct 5 '16 at 10:50
• sorry about that and its $$(x-3)\frac{dy}{dx}-y=(3-x)^2$$ – Kirn Johnson Oct 5 '16 at 11:23
• the thing is i dont understand how to go about doing such question in general i missed the class due to work (PT student) and i was hoping i would be given an explanation on how to go about doing the questions i asked i.e put it in the form and solve – Kirn Johnson Oct 5 '16 at 12:11

## 1 Answer

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 $$y=x(x-3)+C(x-3)$$