Internal problem ID [12261]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 1. Introduction. Exercises page 14
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-2 \sqrt {{| y|}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x)-2*sqrt(abs(y(x)))=0,y(x), singsol=all)
\[ x -\frac {\left (\left \{\begin {array}{cc} -2 \sqrt {-y \left (x \right )} & y \left (x \right )\le 0 \\ 2 \sqrt {y \left (x \right )} & 0<y \left (x \right ) \end {array}\right .\right )}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.291 (sec). Leaf size: 31
DSolve[y'[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*}