Internal problem ID [3654]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 927.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x^{3} \left (y^{\prime }\right )^{2}-a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.187 (sec). Leaf size: 31
dsolve(x^3*diff(y(x),x)^2 = a,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {2 \sqrt {a x}}{x}+c_{1} \\ y \relax (x ) = \frac {2 \sqrt {a x}}{x}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 39
DSolve[x^3 (y'[x])^2==a,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 \sqrt {a}}{\sqrt {x}}+c_1 \\ y(x)\to \frac {2 \sqrt {a}}{\sqrt {x}}+c_1 \\ \end{align*}