# Differential Equations

Fizz_Geek

r" = 1/r^2

## Homework Equations

A friend gave this to me, he was just wondering how we'd approach it.

## The Attempt at a Solution

I don't think the equation is linear, so I don't know how to approach it. My friend suggested integrating both sides with respect to r, but we don't know if that's legal because we don't know what r might be a function of.

Homework Helper
Multiple both sides by r' and that will give you the first integral.

Fizz_Geek
Multiple both sides by r' and that will give you the first integral.

How's does multiplying by a derivative give me an integral?

Homework Helper
As
$$r''=\frac{1}{r^{2}}$$
Multiply both sides by r' to obtain:
$$r'r''=\frac{r'}{r^{2}}\Rightarrow\left(\frac{(r')^{2}}{2}\right) '=\left( -\frac{1}{r}\right) '$$
Integrate easily from here.

Did you try it? What is the derivative of $(r')^2$? So what is the integral of $r' r''$? What is the integral of $dr/r^2$?