Chapter 1.4, Problem 30P

(a)

Program Plan Intro

To find: A general solution of the differential equation ${\left(\frac{dy}{dx}\right)}^2=4y$ and find the points $\left(a,b\right)$ such that the initial value problem ${\left(y^{\prime }\right)}^2=4y$ , $y\left(a\right)=b$ has no solution.

(b)

Program Plan Intro

To find: The initial value problem ${\left(y^{\prime }\right)}^2=4y$ , $y\left(a\right)=b$ has infinitely many solutions that are defined for all $x$ .

(c)

Program Plan Intro

To find: That the initial value problem ${\left(y^{\prime }\right)}^2=4y$ , $y\left(a\right)=b$ hasonly finitely many solutions on some neighborhood of the point $x=a$ .