I have to solve the differential equation (y')^2= 4y to verify the general solution curves and singular solution curves. Determine the points (a,b) in the plane for which the initial value problem (y')^2= 4y, y(a)= b has (a) no solution , (b) infinitely many solutions (that are defined for all values of x ) (c) on some neighborhood of the point x=a , only finitely many solutions. general solution that i am getting is y (x) = (x-c)^2 and singular solution is y(x)=0. I am able to get part (a), as if b < 0, the problem has no solution. Please help me figure out (b) and (c) .