# Finding the general solution to the DE

1. Aug 3, 2010

### x11010

1. The problem statement, all variables and given/known data

(x^2)yy' = e^x

2. Relevant equations

general solution to the DE

3. The attempt at a solution

first i changed y' to dy/dx

(x^2)y(dy/dx) = e^x

then divided both members by x^2 and multiplied both members by dx

ydy = (e^x)dx/(x^2)

or

ydy = (x^-2)(e^x)dx

how do i integrate (x^-2)(e^x)dx?

2. Aug 3, 2010

### Bohrok

∫ex/x2 dx doesn't have an elementary antiderivative. Did you copy down the problem correctly?

3. Aug 4, 2010

### x11010

yeah. i copied it correctly..you may want to take a look at the problem statement..

anyways, are there any methods to solve x-2exdx?

or how do i solve this DE? it is the only problem in my homework that i couldnt slove.

4. Aug 4, 2010

### Gib Z

If you wanted you could integrate by parts to get:

$$\int \frac{e^x}{x^2} dx = Ei (x) - \frac{e^x}{x} + C$$

where Ei(x) is the http://en.wikipedia.org/wiki/Exponential_integral" [Broken]. It doesn't really matter though, as Differential Equations are generally considered solved if your solution is a finite combination of known functions and integrals of known functions.

Last edited by a moderator: May 4, 2017