Internal problem ID [3695]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 970.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{2} \left (y^{\prime }\right )^{2}-a^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 49
dsolve(y(x)^2*diff(y(x),x)^2 = a^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {2 a x +c_{1}} \\ y \relax (x ) = -\sqrt {2 a x +c_{1}} \\ y \relax (x ) = \sqrt {-2 a x +c_{1}} \\ y \relax (x ) = -\sqrt {-2 a x +c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.215 (sec). Leaf size: 85
DSolve[y[x]^2(y'[x])^2==a^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} \sqrt {-a x+c_1} \\ y(x)\to \sqrt {2} \sqrt {-a x+c_1} \\ y(x)\to -\sqrt {2} \sqrt {a x+c_1} \\ y(x)\to \sqrt {2} \sqrt {a x+c_1} \\ \end{align*}