Internal problem ID [6813]
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]
\[ \boxed {{y^{\prime }}^{3}+2 x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 141
dsolve(diff(y(x),x)^3+2*x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {2 \left (-2 x +\sqrt {x^{2}+3 c_{1}}\right ) \sqrt {-6 \sqrt {x^{2}+3 c_{1}}-6 x}}{9} \\ y \left (x \right ) &= -\frac {2 \left (-2 x +\sqrt {x^{2}+3 c_{1}}\right ) \sqrt {-6 \sqrt {x^{2}+3 c_{1}}-6 x}}{9} \\ y \left (x \right ) &= -\frac {2 \left (2 x +\sqrt {x^{2}+3 c_{1}}\right ) \sqrt {6 \sqrt {x^{2}+3 c_{1}}-6 x}}{9} \\ y \left (x \right ) &= \frac {2 \left (2 x +\sqrt {x^{2}+3 c_{1}}\right ) \sqrt {6 \sqrt {x^{2}+3 c_{1}}-6 x}}{9} \\ \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