First order, homogenous DE

Find the values $\displaystyle a$ and $\displaystyle b$ such that the positive function $\displaystyle y(x)$ defined implicitly by the equation $\displaystyle x^a=Ae^{-(xy)^b}$ satisfies $\displaystyle dy/dx+y/x=(5/4)x^3y^5$. Note: $\displaystyle y(1)=2$

Looking for a hint as to how I should tackle this problem. I implicitly differentiated the first equation and ended up with $\displaystyle dy/dx+y/x=(-ax^{a-2})/(Ab(xy)^{b-1})$. I really don't know though. I am stumped.

Re: First order, homogenous DE

Implicit differentiation of the first equation leads to dy/dx which has to be brought back into the ODE.

So, you must not have dy/dx remaining after simplification and the equation becomes very simple. Then, a and b are straightforwards obtained.

Probably, there is a mistake somewhere in your calculus. But without seeing the details of your calculus it is impossible to show you where is the mistake.

Re: First order, homogenous DE

I will hit the drawing boards. Thanks!

Edit: I ended up getting the correct results! Thanks!