(xe^(y/x)+ 2(x^2)y)dy − (ye^(y/x))dx = 0
I've tried solving this equation with no luck. I have tried a variety of different ways but I end up with integrals that are impossible to solve.
Any suggestions would be greatly appreciated. Thanks!
(xe^(y/x)+ 2(x^2)y)dy − (ye^(y/x))dx = 0
I've tried solving this equation with no luck. I have tried a variety of different ways but I end up with integrals that are impossible to solve.
Any suggestions would be greatly appreciated. Thanks!
If you group the terms as follows
$\displaystyle
(x \,dy - y \,dx) e^{y/x} + 2y\,dy = 0
$
then divide by $\displaystyle x^2$ so
$\displaystyle
\frac{x\,dy - y\,dx}{x^2} e^{y/x} + 2y \, dy = 0
$
so
$\displaystyle
d\left(\frac{y}{x} \right) e^{y/x} + d\left(y^2\right) = 0
$
which can be integrated giving
$\displaystyle
e^{y/x} + y^2 = c.
$