71.1.8 problem 22

Internal problem ID [14317]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises page 14
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 06:26:26 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-2 \sqrt {{| y|}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(diff(y(x),x)-2*sqrt(abs(y(x)))=0,y(x), singsol=all)
 

\[ x +\left (\left \{\begin {array}{cc} \sqrt {-y} & y\le 0 \\ -\sqrt {y} & 0<y \end {array}\right .\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.222 (sec). Leaf size: 31

DSolve[D[y[x],x]-Sqrt[Abs[y[x]]]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\sqrt {| K[1]| }}dK[1]\&\right ][x+c_1] \\ y(x)\to 0 \\ \end{align*}