I have to solve the differential equation (y')^2= 4y to verify the general solution curves and singular solution curves.(adsbygoogle = window.adsbygoogle || []).push({});

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) .

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# Differential Equations : Solution Curves

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