Internal problem ID [3574]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 843.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}-a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 25
dsolve(x*diff(y(x),x)^2 = a,y(x), singsol=all)
\begin{align*} y \relax (x ) = 2 \sqrt {a x}+c_{1} \\ y \relax (x ) = -2 \sqrt {a x}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 39
DSolve[x (y'[x])^2==a,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \sqrt {a} \sqrt {x}+c_1 \\ y(x)\to 2 \sqrt {a} \sqrt {x}+c_1 \\ \end{align*}