ODE
\[ y'(x)=\sqrt {| y(x)| } \] ODE Classification
[_quadrature]
Book solution method
Separable ODE, Independent variable missing
Mathematica ✓
cpu = 0.240552 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\sqrt {| K[1]| }}dK[1]\& \right ][x+c_1]\right \}\right \}\]
Maple ✓
cpu = 0.098 (sec), leaf count = 31
\[\left [x -\left (\left \{\begin {array}{cc}-2 \sqrt {-y \left (x \right )} & y \left (x \right )\le 0 \\ 2 \sqrt {y \left (x \right )} & 0<y \left (x \right ) \end {array}\right .\right )+\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[y'[x] == Sqrt[Abs[y[x]]],y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[Inactive[Integrate][1/Sqrt[Abs[K[1]]], {K[1], 1, #1}] & ][x + C[1]]}}
Maple raw input
dsolve(diff(y(x),x) = abs(y(x))^(1/2), y(x))
Maple raw output
[x-piecewise(y(x) <= 0,-2*(-y(x))^(1/2),0 < y(x),2*y(x)^(1/2))+_C1 = 0]