# Understanding Differential Equations

1. Feb 18, 2014

### BOAS

Hello,

these are the first differential equations i've tried to solve...

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

Find the general solution of the following differential equations. In each case if
y = 2 when x = 1 find y when x = 3.

$2x \frac{dy}{dx} = 3$

2. Relevant equations

3. The attempt at a solution

$2x \frac{dy}{dx} = 3$

$\frac{dy}{dx} = \frac{3}{2x}$

$dy = (\frac{3}{2x}) dx$

$\int dy = \int (\frac{3}{2x}) dx$

$y = \frac{3}{2}ln|x| + c$

Firstly, is this correct and secondly, the question says that when y = 2, x = 1 but ln(1) = 0 so I don't see how this can be true. Or have I just found out that my constant of integration, c = 2?

BOAS

2. Feb 18, 2014

### PeroK

I think you've just found the value of your constant of integration!

If you have solved a diff equ, you can always check your answer by diferentiating it and putting it back in the original equation. It's often worth doing if you're not sure.