I am so confused on how to solve this problem. I have it set up with y's on one side and x's on the other but I don't know what to do from there.

Question

Question: Solve the differential equation. The initial condition is y(0) = 1.

((x^2+1)^(1/2))(dy/dx) - (x/(2y)) = 0
y > 0

My work: 2y = (x/(x^2+1)^(1/2))(dx)
Thank You!!

Answer 1

√(x^2+1) dy/dx - x/(2y) = 0
√(x^2+1) dy/dx = x/(2y)
2y dy = x/√(x^2+1) dx
y^2 = √(x^2+1) + c

y(0)=1, so
1 = 1+c
c = 0

y^2 = √(x^2+1)
y = ∜(x^2+1)