Internal problem ID [4255]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1030.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {{y^{\prime }}^{3}+a x y^{\prime }-a y=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 39
dsolve(diff(y(x),x)^3+a*x*diff(y(x),x)-a*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {2 \sqrt {-3 a x}\, x}{9} y \left (x \right ) = \frac {2 \sqrt {-3 a x}\, x}{9} y \left (x \right ) = c_{1} x +\frac {c_{1}^{3}}{a} \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 68
DSolve[(y'[x])^3 +a x y'[x]-a y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1{}^3}{a}+c_1 x y(x)\to -\frac {2 i \sqrt {a} x^{3/2}}{3 \sqrt {3}} y(x)\to \frac {2 i \sqrt {a} x^{3/2}}{3 \sqrt {3}} \end{align*}