Solving an initial value problem

Question

2x-6y√(x²+1)(dy/dx) = 0, where y(0) = -2

Answer 1

This is separable: 6ydy = 2xdx/sqrt(x²+1)

You can take indefinite integral of both sides and solve for C so that y(0) = -2

3y² = 2sqrt(x²+1) + C

or you can take definite integral in y from -2 to y and in x from 0 to x

3y² - 12 = 2sqrt(x²+1) - 2

You can solve for y if you wish.

Please consider a tutor. Take care.