Solution for Differential Equations with x = e^t

[Jenkz]

Homework Statement

ax^{2}\frac{d^{2}y}{dx^{2}}+bx\frac{dy}{dx}+cy=0

Let x= e^{t}

Find \frac{dy}{dx} and \frac{d^{2}y}{dx^{2}} in terms of \frac{dy}{dt} and \frac{d^{2}y}{dt^{2}}

The Attempt at a Solution

if x= e^{t} then \frac{dx}{dt} = e^{t}= x

\frac{dy}{dx}= \frac{dy}{dt}\frac{dt}{dx}= \frac{dy}{dt}\frac{1}{x}

 

[Dick]

(d/dt)=(dx/dt)*(d/dx). It's the chain rule.

 

[Jenkz]

ohh ok! Didn't think of that, I was expecting something more difficult I guess. Thanks :)