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Differential Equations : Solution Curves 
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#1
Aug3111, 03:43 PM

P: 26

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) = (xc)^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
Sep111, 01:07 PM

HW Helper
Thanks
PF Gold
P: 7,657

Think about a function g(x) defined piecewise with g(x) = 0 for x < c and g(x) = (xc)^{2} if x ≥ c.



#3
Sep111, 02:20 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,544

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



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