Question

Solve the separable differential equation 10x−6ysqrt(x^2+1)dy/dx=0. with the initial condition y(0)=4.

Answer 1

10x−6y√(x^2+1)dy/dx=0
6y√(x^2+1) dy/dx = 10x
6y dy = 10x/√(x^2+1) dx
3y^2 = 10√(x^2+1) + c

Since y(0) = 4,
3*16 = 10+c
c = 38

now you have it.