Internal problem ID [2847]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 98.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\sqrt {{| y|}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 31
dsolve(diff(y(x),x) = sqrt(abs(y(x))),y(x), singsol=all)
\[ x -\left (\left \{\begin {array}{cc} -2 \sqrt {-y \relax (x )} & y \relax (x )\le 0 \\ 2 \sqrt {y \relax (x )} & 0<y \relax (x ) \end {array}\right .\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 31
DSolve[y'[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*}