# First order, homogenous DE

• Feb 26th 2013, 11:59 AM
quantoembryo
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.
• Feb 27th 2013, 12:34 AM
JJacquelin
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.
• Feb 27th 2013, 04:00 AM
quantoembryo
Re: First order, homogenous DE
I will hit the drawing boards. Thanks!

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