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Differential Equations : Solution Curves

  1. Aug 31, 2011 #1
    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) .
  2. jcsd
  3. Sep 1, 2011 #2


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    Think about a function g(x) defined piecewise with g(x) = 0 for x < c and g(x) = (x-c)2 if x ≥ c.
  4. Sep 1, 2011 #3


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    For (c) consider the situation when b= 0.
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