Solve the separable differential equation y'(x) = sqrt(2y(x)+15)
and find the particular solution satisfying the initial condition y(1) = -3
So we have the differential equation:
The LHS is just the integral I finished up at the top, so
And we know .
Now to solve for y.
<-- Square both sides:
Now solve this for , square both sides again, solve the polynomial for y, and check the solutions to make sure there are no extra ones in there. It'll keep you busy for a while, to say the least.