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!

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.

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...