Internal problem ID [3461]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 723.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \sqrt {y}-\sqrt {x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 16
dsolve(diff(y(x),x)*sqrt(y(x)) = sqrt(x),y(x), singsol=all)
\[ y \relax (x )^{\frac {3}{2}}-x^{\frac {3}{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 20
DSolve[y'[x] Sqrt[Y]==Sqrt[X],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \sqrt {X}}{\sqrt {Y}}+c_1 \\ \end{align*}