53.3.12 problem 14

Internal problem ID [8474]
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 : 14
Date solved : Monday, January 27, 2025 at 04:06:37 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.073 (sec). Leaf size: 32

dsolve(x^6*diff(y(x),x)^3-3*x*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 123.852 (sec). Leaf size: 24834

DSolve[x^6*(D[y[x],x])^3-3*x*D[y[x],x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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