Internal problem ID [4176]
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]
\[ \boxed {y {y^{\prime }}^{2}=a^{2} x} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) \left (\frac {a^{2} \left (\left (y \left (x \right ) x \right )^{\frac {3}{2}} a -y \left (x \right )^{3}\right )}{y \left (x \right )^{3}}\right )^{\frac {2}{3}}}+x = 0 -\frac {c_{1} x}{y \left (x \right ) \left (-\frac {a^{2} \left (\left (y \left (x \right ) x \right )^{\frac {3}{2}} a +y \left (x \right )^{3}\right )}{y \left (x \right )^{3}}\right )^{\frac {2}{3}}}+x = 0 \end{align*}
✓ Solution by Mathematica
Time used: 3.625 (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*}