During another engineering problem I have encountered the following differential equation $$ y'=\frac{21y+9x}{y+21x} $$
I'm only familier with solving using seperation of the variables but here I have an item of type $y\cdot x$ and $y \cdot y'$ so im not sure how to deal with it.
I'd really appreciate some help. Thanks in advance
Best Answer
HINT
As suggested by @mattos, the proposed ODE is equivalent to \begin{align*} (xu)' = \frac{21u + 9}{u + 21} & \Longleftrightarrow xu' + u - \frac{21u + 9}{u + 21} = 0\\\\ & \Longleftrightarrow xu' + \frac{u^{2} - 9}{u + 21} = 0 \end{align*}
which is separable.
Can you take it from here?