Differential Equations : Solution Curves

by mehtamonica
Tags: curves, differential, equations, solution
mehtamonica is offline
Aug31-11, 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) = (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) .
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
LCKurtz is online now
Sep1-11, 01:07 PM
HW Helper
PF Gold
LCKurtz's Avatar
P: 7,232
Think about a function g(x) defined piecewise with g(x) = 0 for x < c and g(x) = (x-c)2 if x ≥ c.
HallsofIvy is offline
Sep1-11, 02:20 PM
Sci Advisor
PF Gold
P: 38,904
For (c) consider the situation when b= 0.

Register to reply

Related Discussions
Differential equations, qualitative solution Calculus & Beyond Homework 6
differential equations - finding solution Calculus & Beyond Homework 2
Solution to system of differential equations Calculus & Beyond Homework 2
Solution for these Differential equations Calculus & Beyond Homework 11
Solution of Ordinary Differential Equations Physics Learning Materials 0