General and particular solutions help?

Question

Let y= f(x) be the particular solution to the differential equation dy/dx= 1/(2y+1) with the initial condition y(0)= 0. Which of the following gives an expression for f(x) and the domain for which the solution is valid? Please show how to solve it?

A. y= (e^2x-1)/2 for all x

B. y= tanx for -π/2 < x < π/2

C. y= √x for x≥0

D. y= (-1+√1+4x)/2 for x> -1/4

Answer 1

The solution of the DE (which is of variables separable type) is y² + y = x.

You solve it from there.