53.3.17 problem 20

Internal problem ID [8479]
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 : 20
Date solved : Monday, January 27, 2025 at 04:07:06 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 58

dsolve(2*diff(y(x),x)^3+x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {\left (-c_{1}^{2}-24 x \right ) \sqrt {c_{1}^{2}+24 x}}{432}-\frac {c_{1}^{3}}{432}-\frac {c_{1} x}{12} \\ y &= \frac {\left (c_{1}^{2}+24 x \right )^{{3}/{2}}}{432}-\frac {c_{1}^{3}}{432}-\frac {c_{1} x}{12} \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Timed out