how do i solveseparable differential equation

Question

7x−4y sqrt(x^2+1) dxdy=0
Subject to the initial condition: y(0)=−10

Answer 1

Is that dx/dy or dy/dx in your equation?

If it is dx/dy, rewrite it as
7x − 4y sqrt(x^2+1) dx/dy = 0 as
7x = 4y sqrt(x^2+1) dx/dy
which can be separated as
(1/7x)*sqrt(x^2+1) dx = dy/4y

Now integrate both sides separately.