Internal problem ID [6054]
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: 15.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y-x^{6} \left (y^{\prime }\right )^{3}+x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.422 (sec). Leaf size: 28
dsolve(y(x)=x^6*diff(y(x),x)^3-x*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1}^{6}-\sqrt {\frac {c_{1}^{2}}{x^{2}}}\, c_{1} \\ y \relax (x ) = \frac {c_{1}}{x^{\frac {3}{2}}} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]==x^6*(y'[x])^3-x*y'[x],y[x],x,IncludeSingularSolutions -> True]
Timed out