66.2.35 problem Problem 50

Internal problem ID [13934]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 50
Date solved : Tuesday, January 28, 2025 at 06:09:07 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} {y^{\prime \prime }}^{3}+y^{\prime \prime }+1&=x \end{align*}

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 222

dsolve(diff(y(x),x$2)^3+diff(y(x),x$2)+1=x,y(x), singsol=all)
 

\begin{align*} y &= \frac {\left (\int \left (\int \frac {\left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{{2}/{3}}-12}{\left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{{1}/{3}}}d x \right )d x \right )}{6}+c_{1} x +c_{2} \\ y &= -\frac {\left (\int \left (\int \frac {i \sqrt {3}\, \left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{{2}/{3}}+12 i \sqrt {3}+\left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{{2}/{3}}-12}{\left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{{1}/{3}}}d x \right )d x \right )}{12}+c_{1} x +c_{2} \\ y &= \frac {\left (\int \left (\int \frac {\left (i \sqrt {3}-1\right ) \left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{{2}/{3}}+12 i \sqrt {3}+12}{\left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{{1}/{3}}}d x \right )d x \right )}{12}+c_{1} x +c_{2} \\ \end{align*}

✗ Solution by Mathematica

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

DSolve[D[y[x],{x,2}]^3+D[y[x],{x,2}]+1==x,y[x],x,IncludeSingularSolutions -> True]
 

Timed out