7.3.30 problem 30

Internal problem ID [70]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 30
Date solved : Friday, February 07, 2025 at 07:47:46 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}&=4 y \end{align*}

With initial conditions

\begin{align*} y \left (a \right )&=b \end{align*}

✓ Solution by Maple

Time used: 0.165 (sec). Leaf size: 53

dsolve([diff(y(x),x)^2= 4*y(x),y(a) = b],y(x), singsol=all)
 

\begin{align*} y &= \left (-2 a +2 x \right ) \sqrt {b}+a^{2}-2 x a +x^{2}+b \\ y &= \left (2 a -2 x \right ) \sqrt {b}+a^{2}-2 x a +x^{2}+b \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 33

DSolve[{D[y[x],x]^2== 4*y[x],{y[a]==b}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \left (a+\sqrt {b}-x\right )^2 \\ y(x)\to \left (-a+\sqrt {b}+x\right )^2 \\ \end{align*}