Internal problem ID [6044]
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: 5.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x \left (y^{\prime }\right )^{3}-6 y \left (y^{\prime }\right )^{2}+x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 1.422 (sec). Leaf size: 71
dsolve(2*x*diff(y(x),x)^3-6*y(x)*diff(y(x),x)^2+x^4=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{2}}{2} \\ y \relax (x ) = \frac {1}{6 c_{1}^{2}}+\frac {x^{3} c_{1}}{3} \\ y \relax (x ) = \frac {x^{2} \left (\sqrt {3}\, \tan \left (\RootOf \left (-\sqrt {3}\, \ln \left (\frac {3 x^{4}}{4}+\frac {3 x^{4} \left (\tan ^{2}\left (\textit {\_Z} \right )\right )}{4}\right )+4 \sqrt {3}\, c_{1}-2 \textit {\_Z} \right )\right )-1\right )}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 94.037 (sec). Leaf size: 21360
DSolve[2*x*(y'[x])^3-6*y[x]*(y'[x])^2+x^4==0,y[x],x,IncludeSingularSolutions -> True]
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