(a) Verify that all members of the family are solutions of the differential equation.

(b) Find a solution of the initial-value problem.

I do not know how to solve a. However, This is how I solved b. Please give me a hint to solve a and check my answer for b.

(b)

Move the ys to one side:

Integrate:

I dont think my answer is correct.

Edit: Added the C.