53.3.19 problem 22

Internal problem ID [8481]
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 equation. EXERCISES Page 320
Problem number : 22
Date solved : Monday, January 27, 2025 at 04:07:08 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} {y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.033 (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 &= \frac {2 \left (-2 x +\sqrt {x^{2}+3 c_{1}}\right ) \sqrt {-6 \sqrt {x^{2}+3 c_{1}}-6 x}}{9} \\ y &= -\frac {2 \left (-2 x +\sqrt {x^{2}+3 c_{1}}\right ) \sqrt {-6 \sqrt {x^{2}+3 c_{1}}-6 x}}{9} \\ y &= -\frac {2 \left (2 x +\sqrt {x^{2}+3 c_{1}}\right ) \sqrt {6 \sqrt {x^{2}+3 c_{1}}-6 x}}{9} \\ y &= \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: 0.000 (sec). Leaf size: 0

DSolve[(D[y[x],x])^3+2*x*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out