Internal problem ID [3752]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1038.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}+{\mathrm e}^{-2 y+3 x} \left (y^{\prime }-1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 118.453 (sec). Leaf size: 540
dsolve(diff(y(x),x)^3+exp(3*x-2*y(x))*(diff(y(x),x)-1) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {3 x}{2}+\RootOf \left (-x -2 \left (\int _{}^{\textit {\_Z}}\frac {{\mathrm e}^{2 \textit {\_a}} \left (18 \sqrt {12 \,{\mathrm e}^{-6 \textit {\_a}}+81 \,{\mathrm e}^{-4 \textit {\_a}}}+162 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}}}{-2 \left (\sqrt {12 \,{\mathrm e}^{-6 \textit {\_a}}+81 \,{\mathrm e}^{-4 \textit {\_a}}}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {2}{3}} {\mathrm e}^{2 \textit {\_a}}+3 \,{\mathrm e}^{2 \textit {\_a}} \left (18 \sqrt {12 \,{\mathrm e}^{-6 \textit {\_a}}+81 \,{\mathrm e}^{-4 \textit {\_a}}}+162 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}}+2 \,12^{\frac {1}{3}}}d \textit {\_a} \right )+c_{1}\right ) \\ y \relax (x ) = \frac {3 x}{2}+\RootOf \left (-x -12 i \left (\int _{}^{\textit {\_Z}}\frac {{\mathrm e}^{2 \textit {\_a} +3} \left (\sqrt {4 \,{\mathrm e}^{-6 \textit {\_a}}+27 \,{\mathrm e}^{-4 \textit {\_a}}}+3 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}}}{-2 \,{\mathrm e}^{2 \textit {\_a} +3} \left (6 \,{\mathrm e}^{-6 \textit {\_a}}+81 \,{\mathrm e}^{-4 \textit {\_a}}+9 \,{\mathrm e}^{-2 \textit {\_a}} \sqrt {12 \,{\mathrm e}^{-6 \textit {\_a}}+81 \,{\mathrm e}^{-4 \textit {\_a}}}\right )^{\frac {1}{3}} 3^{\frac {5}{6}}+18 i 3^{\frac {1}{6}} \left (\sqrt {4 \,{\mathrm e}^{-6 \textit {\_a}}+27 \,{\mathrm e}^{-4 \textit {\_a}}}+3 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}} {\mathrm e}^{2 \textit {\_a} +3}+2 i {\mathrm e}^{2 \textit {\_a} +3} \left (18 \,{\mathrm e}^{-6 \textit {\_a}}+243 \,{\mathrm e}^{-4 \textit {\_a}}+27 \,{\mathrm e}^{-2 \textit {\_a}} \sqrt {12 \,{\mathrm e}^{-6 \textit {\_a}}+81 \,{\mathrm e}^{-4 \textit {\_a}}}\right )^{\frac {1}{3}}-2 i {\mathrm e}^{3} 18^{\frac {1}{3}}-6 \,{\mathrm e}^{3} 3^{\frac {1}{6}} 2^{\frac {1}{3}}}d \textit {\_a} \right ) 3^{\frac {1}{6}}+c_{1}\right ) \\ y \relax (x ) = \frac {3 x}{2}+\RootOf \left (-x +12 i \left (\int _{}^{\textit {\_Z}}-\frac {{\mathrm e}^{2 \textit {\_a} +3} \left (\sqrt {4 \,{\mathrm e}^{-6 \textit {\_a}}+27 \,{\mathrm e}^{-4 \textit {\_a}}}+3 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}}}{2 \left ({\mathrm e}^{2 \textit {\_a} +3} \left (6 \,{\mathrm e}^{-6 \textit {\_a}}+81 \,{\mathrm e}^{-4 \textit {\_a}}+9 \,{\mathrm e}^{-2 \textit {\_a}} \sqrt {12 \,{\mathrm e}^{-6 \textit {\_a}}+81 \,{\mathrm e}^{-4 \textit {\_a}}}\right )^{\frac {1}{3}} 3^{\frac {5}{6}}+9 i 3^{\frac {1}{6}} \left (\sqrt {4 \,{\mathrm e}^{-6 \textit {\_a}}+27 \,{\mathrm e}^{-4 \textit {\_a}}}+3 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}} {\mathrm e}^{2 \textit {\_a} +3}+i {\mathrm e}^{2 \textit {\_a} +3} \left (18 \,{\mathrm e}^{-6 \textit {\_a}}+243 \,{\mathrm e}^{-4 \textit {\_a}}+27 \,{\mathrm e}^{-2 \textit {\_a}} \sqrt {12 \,{\mathrm e}^{-6 \textit {\_a}}+81 \,{\mathrm e}^{-4 \textit {\_a}}}\right )^{\frac {1}{3}}-i {\mathrm e}^{3} 18^{\frac {1}{3}}+3 \,{\mathrm e}^{3} 3^{\frac {1}{6}} 2^{\frac {1}{3}}\right )}d \textit {\_a} \right ) 3^{\frac {1}{6}}+c_{1}\right ) \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y'[x])^3 +Exp[3 x -2 y[x]](y'[x]-1)==0,y[x],x,IncludeSingularSolutions -> True]
Timed out