# Math Help - epproach on solving this equation

1. ## epproach on solving this equation

$xy'-2x^{2}\sqrt{y}=4y$
this equation in not saparable so i need to find the integration coefficient?

is there easier way
it looks like bernuly but i am not sure
because of the square root

2. If by "integration coefficient" you mean "integrating factor", that technique only works on first-order linear equations, which this obviously is not. Why not try the Bernoulli approach? Standard form would be

$xy'-2x^{2}\sqrt{y}=4y$

$xy'-4y=2x^{2}\sqrt{y}$

$y'-\dfrac{4}{x}\,y=2x\sqrt{y}=2xy^{1/2}.$

So the substitution would be what?

3. Setting $z=\sqrt{y} \implies dy=2\ z\ dz$ You obtain...

$\displaystyle z^{'} = 2\ \frac{z}{x} +x$ (1)

... that is a linear first order ODE and can be 'attacked' in usual way...

Kind regards

$\chi$ $\sigma$

4. thanks

5. You're welcome for my contribution. Incidentally, I believe that the Bernoulli approach would use the same substitution that chisigma proposed.