# Math Help - graphing problem

1. ## graphing problem

I have a question for a problem in my homework. I was given the following differential equation

$\frac{dr}{d\theta} = \frac{r^2}{\theta}

$

r(1) = 2

When i solved the equation I get

$\frac{1}{ln\theta} = r

$

My question is how do I go for solving for c? I know to just plug in 2 for r and 1 for theta. Is this problem in polar form? I have not covered polar form in any of my classes so that is where I think I am lost. any help would be appreciated.

2. $\frac{dr}{d\theta} = \frac{r^2}{\theta}$

$\frac{dr}{r^2}=\frac{d\theta}{\theta}$

Integrating both sides,

$-\frac{1}{r}=ln \theta+C$ ------ (1)

$r(1)=2$

Substituting in (1) we get,

$-\frac{1}{2}=ln 1+C$

$C=-\frac{1}{2}$

Hence,

$-\frac{1}{r}=ln \theta-\frac{1}{2}$