Internal problem ID [6058]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 99. Clairaut’s equation. EXERCISES Page
320
Problem number: 20.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
Solve \begin {gather*} \boxed {2 \left (y^{\prime }\right )^{3}+x y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.281 (sec). Leaf size: 79
dsolve(2*diff(y(x),x)^3+x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (-\frac {c_{1}}{12}-\frac {\sqrt {c_{1}^{2}+24 x}}{12}\right )^{3}+\frac {\left (-\frac {c_{1}}{12}-\frac {\sqrt {c_{1}^{2}+24 x}}{12}\right ) x}{2} \\ y \relax (x ) = \left (-\frac {c_{1}}{12}+\frac {\sqrt {c_{1}^{2}+24 x}}{12}\right )^{3}+\frac {\left (-\frac {c_{1}}{12}+\frac {\sqrt {c_{1}^{2}+24 x}}{12}\right ) x}{2} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[2*(y'[x])^3+x*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out