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 :)