Thread: Differential equation

Help I have no clue how to tackle this question:

Find the particular solution of:

dy/dx - 1/x y = x^2 - 3, y(1) = 1/2

Please can anyone give me some help with this one?

Any help would be appreciated!!

Thank you.

This is a pretty standard First Order Differential equation.

the integrating factor is $\displaystyle I.F = e^{ \int \frac{-1}{x}}$

I will leave you to simply that.
then you should know that $\displaystyle \frac{d}{dx} \left ( y \cdot I.F \right ) = I.F (x^2-3)$

and the rest should be easy, dont forget your constant for integration.