# Homogenous D.E. with Non-Constant Coefficients

• Oct 12th 2011, 03:40 PM
jegues
Homogenous D.E. with Non-Constant Coefficients
How do I go about solving this differential equation?

I can't remember if we even covered this in my calculus class, but as soon as I see the solution it should jog my memory.

$\displaystyle 0 = 4\frac{dy}{dx} + x\frac{d^{2}y}{(dx)^{2}} \quad \text{where} \quad y=f(x)$

Thanks again!
• Oct 12th 2011, 03:45 PM
Jester
Re: Homogenous D.E. with Non-Constant Coefficients
Since your ODE has no $\displaystyle y$, if you let $\displaystyle \dfrac{dy}{dx} = u$ then $\displaystyle \dfrac{d^2y}{dx^2} = \dfrac{d u}{d x}$ and substitute, your ODE will separate.
• Oct 12th 2011, 08:42 PM
Prove It
Re: Homogenous D.E. with Non-Constant Coefficients
Quote:

Originally Posted by Danny
Since your ODE has no $\displaystyle y$, if you let $\displaystyle \dfrac{dy}{dx} = u$ then $\displaystyle \dfrac{d^2y}{dx^2} = \dfrac{d u}{d x}$ and substitute, your ODE will separate.

And is also first-order linear...