Internal problem ID [12198]
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.
ODE order: 2.
ODE degree: 3.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {{y^{\prime \prime }}^{3}+y^{\prime \prime }=x -1} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 226
dsolve(diff(y(x),x$2)^3+diff(y(x),x$2)+1=x,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (\int \int \frac {\left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{\frac {2}{3}}-12}{\left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{\frac {1}{3}}}d x d x \right )}{6}+c_{1} x +c_{2} \\ y \left (x \right ) &= -\frac {\left (\int \int \frac {i \sqrt {3}\, \left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{\frac {2}{3}}+12 i \sqrt {3}+\left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{\frac {2}{3}}-12}{\left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{\frac {1}{3}}}d x d x \right )}{12}+c_{1} x +c_{2} \\ y \left (x \right ) &= \frac {\left (\int \int \frac {\left (i \sqrt {3}-1\right ) \left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{\frac {2}{3}}+12 i \sqrt {3}+12}{\left (-108+108 x +12 \sqrt {81 x^{2}-162 x +93}\right )^{\frac {1}{3}}}d x d x \right )}{12}+c_{1} x +c_{2} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x]^3+y''[x]+1==x,y[x],x,IncludeSingularSolutions -> True]
Timed out