Internal problem ID [10779]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 16.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x -{y^{\prime }}^{3}+y^{\prime }-2=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 231
dsolve(x=diff(y(x),x)^3-diff(y(x),x)+2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \int \frac {i \left (i \left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{\frac {2}{3}}-\left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{\frac {2}{3}} \sqrt {3}+12 i+12 \sqrt {3}\right )}{12 \left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{\frac {1}{3}}}d x +c_{1} \\ y \left (x \right ) = \int \frac {i \left (\left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{\frac {2}{3}} \sqrt {3}-12 \sqrt {3}+i \left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{\frac {2}{3}}+12 i\right )}{12 \left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{\frac {1}{3}}}d x +c_{1} \\ y \left (x \right ) = \int \frac {\left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{\frac {2}{3}}+12}{6 \left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{\frac {1}{3}}}d x +c_{1} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x==y'[x]^3-y'[x]+2,y[x],x,IncludeSingularSolutions -> True]
Timed out