Internal problem ID [3747]
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]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}+y^{\prime } a x -a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 23
dsolve(diff(y(x),x)^3+a*x*diff(y(x),x)-a*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} x +\frac {c_{1}^{3}}{a} \\ y \relax (x ) = x^{\frac {3}{2}} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (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*}