# Find a particular solution that satisfies the intial condition

1. Nov 24, 2009

### Ki-nana18

1. The problem statement, all variables and given/known data
2xy'-ln x2=0 y(1)=2

2. Relevant equations

3. The attempt at a solution
2x(dy/dx)-ln x2=0

I think I'm suppose to separate variables and then integrate next but I'm not sure.

2. Nov 24, 2009

### Staff: Mentor

Yes, this is a separable differential equation.

You should use the fact that ln(x2) = 2ln(x).

2x*dy/dx = 2 ln(x)
$$\Rightarrow~dy~=~ \frac{ln(x)}{x}dx$$

Now integrate both sides. Don't forget the constant of integration, which you will determine from your initial condition, y(1) = 2.