Internal problem ID [3668]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 32
Problem number: 942.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y \left (y^{\prime }\right )^{2}-x \,a^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 74
dsolve(y(x)*diff(y(x),x)^2 = a^2*x,y(x), singsol=all)
\begin{align*} -\frac {c_{1} x}{y \relax (x ) \left (\frac {a^{2} \left (\left (x y \relax (x )\right )^{\frac {3}{2}} a -y \relax (x )^{3}\right )}{y \relax (x )^{3}}\right )^{\frac {2}{3}}}+x = 0 \\ -\frac {c_{1} x}{y \relax (x ) \left (-\frac {a^{2} \left (\left (x y \relax (x )\right )^{\frac {3}{2}} a +y \relax (x )^{3}\right )}{y \relax (x )^{3}}\right )^{\frac {2}{3}}}+x = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.83 (sec). Leaf size: 46
DSolve[y[x] (y'[x])^2==a^2 x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (-a x^{3/2}+\frac {3 c_1}{2}\right ){}^{2/3} \\ y(x)\to \left (a x^{3/2}+\frac {3 c_1}{2}\right ){}^{2/3} \\ \end{align*}