Internal problem ID [6055]
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: 16.
ODE order: 1.
ODE degree: 4.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{4}-2 y \left (y^{\prime }\right )^{3}+12 x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.625 (sec). Leaf size: 62
dsolve(x*diff(y(x),x)^4-2*y(x)*diff(y(x),x)^3+12*x^3=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {2 \sqrt {-6 x}\, x}{3} \\ y \relax (x ) = \frac {2 \sqrt {-6 x}\, x}{3} \\ y \relax (x ) = -\frac {2 \sqrt {6}\, x^{\frac {3}{2}}}{3} \\ y \relax (x ) = \frac {2 \sqrt {6}\, x^{\frac {3}{2}}}{3} \\ y \relax (x ) = 6 c_{1}^{3}+\frac {x^{2}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 142.632 (sec). Leaf size: 30947
DSolve[x*(y'[x])^4-2*y[x]*(y'[x])^3+12*x^3==0,y[x],x,IncludeSingularSolutions -> True]
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