General solution of 2x dy/dx = 3 with initial condition

[BOAS]

Hello,

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

Homework Statement

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

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

Homework Equations

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?

Thanks for any help you can give!

BOAS

 

[PeroK]

Or have I just found out that my constant of integration, c = 2?

BOAS

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.