29.32.8 problem 942

Internal problem ID [5520]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 32
Problem number : 942
Date solved : Monday, January 27, 2025 at 11:35:08 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y {y^{\prime }}^{2}&=a^{2} x \end{align*}

✓ Solution by Maple

Time used: 0.063 (sec). Leaf size: 78

dsolve(y(x)*diff(y(x),x)^2 = a^2*x,y(x), singsol=all)
 

\begin{align*} x \left (1-\frac {c_{1}}{\left (-\frac {a^{2} \left (-a x \sqrt {x y \left (x \right )}+y \left (x \right )^{2}\right )}{y \left (x \right )^{2}}\right )^{{2}/{3}} y \left (x \right )}\right ) &= 0 \\ x \left (1-\frac {c_{1}}{\left (-\frac {a^{2} \left (a x \sqrt {x y \left (x \right )}+y \left (x \right )^{2}\right )}{y \left (x \right )^{2}}\right )^{{2}/{3}} y \left (x \right )}\right ) &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.878 (sec). Leaf size: 46

DSolve[y[x] (D[y[x],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*}