Internal problem ID [6062]
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: 24.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}-x y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 83
dsolve(diff(y(x),x)^3-x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\left (\frac {c_{1}}{6}-\frac {\sqrt {c_{1}^{2}-12 x}}{6}\right )^{3}}{2}+\frac {\left (\frac {c_{1}}{6}-\frac {\sqrt {c_{1}^{2}-12 x}}{6}\right ) x}{2} \\ y \relax (x ) = -\frac {\left (\frac {c_{1}}{6}+\frac {\sqrt {c_{1}^{2}-12 x}}{6}\right )^{3}}{2}+\frac {\left (\frac {c_{1}}{6}+\frac {\sqrt {c_{1}^{2}-12 x}}{6}\right ) x}{2} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y'[x])^3-x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out