Internal problem ID [3741]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 34
Problem number: 1024.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}+y^{\prime }-{\mathrm e}^{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 265
dsolve(diff(y(x),x)^3+diff(y(x),x) = exp(y(x)),y(x), singsol=all)
\begin{align*} x -\left (\int _{}^{y \relax (x )}\frac {6 \left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}}{\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {2}{3}}-12}d \textit {\_a} \right )-c_{1} = 0 \\ x -\left (\int _{}^{y \relax (x )}\frac {12 \left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}}{\left (1+i \sqrt {3}\right ) \left (\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}+3 i-\sqrt {3}\right ) \left (-\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}+3 i-\sqrt {3}\right )}d \textit {\_a} \right )-c_{1} = 0 \\ x -\left (\int _{}^{y \relax (x )}-\frac {12 \left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}}{\left (-1+i \sqrt {3}\right ) \left (\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}+\sqrt {3}+3 i\right ) \left (-\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{\frac {1}{3}}+3 i+\sqrt {3}\right )}d \textit {\_a} \right )-c_{1} = 0 \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y'[x])^3 +y'[x]==Exp[ y[x]],y[x],x,IncludeSingularSolutions -> True]
Timed out