Internal problem ID [6060]
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: 22.
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}+2 x y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.281 (sec). Leaf size: 173
dsolve(diff(y(x),x)^3+2*x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\left (-6 \sqrt {x^{2}+3 c_{1}}-6 x \right )^{\frac {3}{2}}}{27}-\frac {2 \sqrt {-6 \sqrt {x^{2}+3 c_{1}}-6 x}\, x}{3} \\ y \relax (x ) = \frac {\left (-6 \sqrt {x^{2}+3 c_{1}}-6 x \right )^{\frac {3}{2}}}{27}+\frac {2 \sqrt {-6 \sqrt {x^{2}+3 c_{1}}-6 x}\, x}{3} \\ y \relax (x ) = -\frac {\left (6 \sqrt {x^{2}+3 c_{1}}-6 x \right )^{\frac {3}{2}}}{27}-\frac {2 \sqrt {6 \sqrt {x^{2}+3 c_{1}}-6 x}\, x}{3} \\ y \relax (x ) = \frac {\left (6 \sqrt {x^{2}+3 c_{1}}-6 x \right )^{\frac {3}{2}}}{27}+\frac {2 \sqrt {6 \sqrt {x^{2}+3 c_{1}}-6 x}\, x}{3} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y'[x])^3+2*x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out