29.4.9 problem 98

Internal problem ID [4700]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 98
Date solved : Monday, January 27, 2025 at 09:32:16 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

dsolve(diff(y(x),x) = sqrt(abs(y(x))),y(x), singsol=all)
 

\[ x +2 \left (\left \{\begin {array}{cc} \sqrt {-y \left (x \right )} & y \left (x \right )\le 0 \\ -\sqrt {y \left (x \right )} & 0<y \left (x \right ) \end {array}\right .\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.195 (sec). Leaf size: 31

DSolve[D[y[x],x]==Sqrt[Abs[y[x]]],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*}