differential equations: solve the initial value problem
x2y' - xy = 2
y(1) = 1

Step-by-step explanation:

Divide both sides of the equation by :

Find the integrating factor:

Multiply the equation by the integrating factor:

The left side is the derivative of (xy), therefore we can write the equation as:

That is a separable equation. We separate and integrate:

We get:

Then plug the initial value y(1)=1, which means to plug x=1 and y=1:

Therefore, the solution once we plug C=1 becomes:

Then solving for y by dividing both sides by x, we get: