66.1.16 problem Problem 16

Internal problem ID [13863]
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
Date solved : Tuesday, January 28, 2025 at 06:06:01 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 207

dsolve(x=diff(y(x),x)^3-diff(y(x),x)+2,y(x), singsol=all)
 

\begin{align*} y &= \frac {\left (\int \frac {\left (i \sqrt {3}-1\right ) \left (108 x -216+12 \sqrt {81 x^{2}-324 x +312}\right )^{{2}/{3}}-12 i \sqrt {3}-12}{\left (108 x -216+12 \sqrt {81 x^{2}-324 x +312}\right )^{{1}/{3}}}d x \right )}{12}+c_{1} \\ y &= -\frac {\left (\int \frac {i \sqrt {3}\, \left (108 x -216+12 \sqrt {81 x^{2}-324 x +312}\right )^{{2}/{3}}-12 i \sqrt {3}+\left (108 x -216+12 \sqrt {81 x^{2}-324 x +312}\right )^{{2}/{3}}+12}{\left (108 x -216+12 \sqrt {81 x^{2}-324 x +312}\right )^{{1}/{3}}}d x \right )}{12}+c_{1} \\ y &= \frac {\left (\int \frac {\left (108 x -216+12 \sqrt {81 x^{2}-324 x +312}\right )^{{2}/{3}}+12}{\left (108 x -216+12 \sqrt {81 x^{2}-324 x +312}\right )^{{1}/{3}}}d x \right )}{6}+c_{1} \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Timed out