Finding the general solution to the DE

[x11010]

Homework Statement

(x^2)yy' = e^x

Homework Equations

general solution to the DE

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?

 

[Bohrok]

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

 

[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^-2e^xdx?

or how do i solve this DE? it is the only problem in my homework that i couldn't slove.

 

[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" . 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.