Internal problem ID [6797]
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]]
\[ \boxed {2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}=-x^{4}} \]
✓ Solution by Maple
Time used: 0.328 (sec). Leaf size: 56
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 \left (x \right ) &= -\frac {\left (1+i \sqrt {3}\right ) x^{2}}{4} \\ y \left (x \right ) &= \frac {\left (i \sqrt {3}-1\right ) x^{2}}{4} \\ y \left (x \right ) &= \frac {x^{2}}{2} \\ y \left (x \right ) &= \frac {1}{6 c_{1}^{2}}+\frac {c_{1} x^{3}}{3} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[2*x*(y'[x])^3-6*y[x]*(y'[x])^2+x^4==0,y[x],x,IncludeSingularSolutions -> True]
Timed out