53.3.13 problem 15

Internal problem ID [8475]
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 : 15
Date solved : Monday, January 27, 2025 at 04:06:48 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y&=x^{6} {y^{\prime }}^{3}-x y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.293 (sec). Leaf size: 36

dsolve(y(x)=x^6*diff(y(x),x)^3-x*diff(y(x),x),y(x), singsol=all)
 

\begin{align*} y &= -\frac {2 \sqrt {3}}{9 x^{{3}/{2}}} \\ y &= \frac {2 \sqrt {3}}{9 x^{{3}/{2}}} \\ y &= c_{1}^{3}-\frac {c_{1}}{x} \\ \end{align*}

✗ Solution by Mathematica

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

DSolve[y[x]==x^6*(D[y[x],x])^3-x*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

Timed out