# Thread: problems of differntial equation

1. ## problems of differntial equation

i got stucked at part 2 now... how should i continue?

2. ## Re: problems of differntial equation

You need to use your solution to part 1 to solve part 2.

You know \displaystyle \begin{align*} \frac{\mathrm{d}z}{\mathrm{d}x} = \frac{4z}{x} + 2 \end{align*}. Rewrite it as \displaystyle \begin{align*} \frac{\mathrm{d}z}{\mathrm{d}x} + \frac{4}{x}\,z = 2 \end{align*}. This is first order linear, so you can solve for \displaystyle \begin{align*} z \end{align*} using the integrating factor method.

Once you have \displaystyle \begin{align*} z \end{align*}, you can get to solution to the original DE because you know \displaystyle \begin{align*} y = \frac{1}{x} + \frac{1}{z} \end{align*}.