Internal problem ID [12129]
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 18.
ODE order: 1.
ODE degree: 4.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y-{y^{\prime }}^{4}+{y^{\prime }}^{3}=-2} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 247
dsolve(y(x)=diff(y(x),x)^4-diff(y(x),x)^3-2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -2 \\ y \left (x \right ) &= \frac {12 \left (\frac {243}{16384}+\frac {\left (\frac {9}{64}-c_{1} +x \right ) \sqrt {64}\, \sqrt {\left (x -c_{1} +\frac {9}{32}\right ) \left (x -c_{1} \right )}}{16}+\frac {c_{1}^{2}}{2}+\left (-\frac {9}{64}-x \right ) c_{1} +\frac {x^{2}}{2}+\frac {9 x}{64}\right ) \left (27-192 c_{1} +192 x +24 \sqrt {64}\, \sqrt {\left (x -c_{1} +\frac {9}{32}\right ) \left (x -c_{1} \right )}\right )^{\frac {2}{3}}+24 \left (x -c_{1} -\frac {7949}{1536}\right ) \left (\frac {9}{64}-c_{1} +x +\frac {\sqrt {64}\, \sqrt {\left (x -c_{1} +\frac {9}{32}\right ) \left (x -c_{1} \right )}}{8}\right ) \left (27-192 c_{1} +192 x +24 \sqrt {64}\, \sqrt {\left (x -c_{1} +\frac {9}{32}\right ) \left (x -c_{1} \right )}\right )^{\frac {1}{3}}+\frac {27 \left (\frac {9}{64}-c_{1} +x \right ) \sqrt {64}\, \sqrt {\left (x -c_{1} +\frac {9}{32}\right ) \left (x -c_{1} \right )}}{2}+108 \left (x -c_{1} +\frac {9}{128}\right ) \left (x -c_{1} +\frac {27}{128}\right )}{\left (27-192 c_{1} +192 x +24 \sqrt {64}\, \sqrt {\left (x -c_{1} +\frac {9}{32}\right ) \left (x -c_{1} \right )}\right )^{\frac {1}{3}} \left (9-64 c_{1} +64 x +8 \sqrt {64}\, \sqrt {\left (x -c_{1} +\frac {9}{32}\right ) \left (x -c_{1} \right )}\right )} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]==y'[x]^4-y'[x]^3-2,y[x],x,IncludeSingularSolutions -> True]
Timed out