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.