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]
\[ \boxed {{y^{\prime }}^{3}+a x y^{\prime }-y a=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 46
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}\, \sqrt {-a x}\, x}{9} \\ y \left (x \right ) &= \frac {2 \sqrt {3}\, \sqrt {-a x}\, x}{9} \\ y \left (x \right ) &= \frac {c_{1} \left (a x +c_{1}^{2}\right )}{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*}