Find a particular solution that satisfies the intial condition

[Ki-nana18]

Homework Statement

2xy'-ln x²=0 y(1)=2

Homework Equations

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.

 

[Mark44]

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.