66.1.18 problem Problem 18

Internal problem ID [13865]
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
Date solved : Tuesday, January 28, 2025 at 06:06:08 AM
CAS classification : [_quadrature]

\begin{align*} y&={y^{\prime }}^{4}-{y^{\prime }}^{3}-2 \end{align*}

✓ 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 &= -2 \\ y &= \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 {9 x}{64}+\frac {x^{2}}{2}\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 )^{{2}/{3}}+24 \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 (x -c_{1} -\frac {7949}{1536}\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 )^{{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 )^{{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: 0.000 (sec). Leaf size: 0

DSolve[y[x]==D[y[x],x]^4-D[y[x],x]^3-2,y[x],x,IncludeSingularSolutions -> True]
 

Timed out