Internal problem ID [6806]
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: 14.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y=0} \]
✓ Solution by Maple
Time used: 0.093 (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 \left (x \right ) &= -\frac {2}{3 x^{\frac {3}{2}}} \\ y \left (x \right ) &= \frac {2}{3 x^{\frac {3}{2}}} \\ y \left (x \right ) &= \frac {c_{1}^{3}}{3}-\frac {c_{1}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 136.42 (sec). Leaf size: 24834
DSolve[x^6*(y'[x])^3-3*x*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
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