I'm trying to find the general solution to the following first order differential equation:
$$y'=-\frac{2}{y}-\frac{3y}{2x}$$
I've tried using various substitutions but these don't seem to be helping. Can anyone suggest how to start this?
Find the general solution of $y'=\frac{-2}{y}-\frac{3y}{2x}$
1
$\begingroup$
ordinary-differential-equations
-
0set $$y=xu$$ to solve the equation, it is a Bernoulli equation – 2017-01-26
1 Answers
6
\begin{eqnarray} y'=-\frac{2}{y}-\frac{3y}{2x}&&\\ 2xyy'+4x+3y^2&=&0\\ x(y^2)'+4x+3(y^2)&=&0\hspace{2cm}(y^2=u)\\ u'+\frac{3}{x}u&=&-4 \end{eqnarray} which is a differential equation of first order.