Internal problem ID [4260]
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]
\[ \boxed {{y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right )=0} \]
✓ Solution by Maple
Time used: 7.391 (sec). Leaf size: 944
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 \left (x \right ) &= \frac {3 x}{2}+\operatorname {RootOf}\left (x +2 \,2^{\frac {1}{3}} 3^{\frac {2}{3}} \left (\int _{}^{\textit {\_Z}}\frac {{\mathrm e}^{2 \textit {\_a}} {\left (\left (\sqrt {3}\, \sqrt {\left (4+27 \,{\mathrm e}^{2 \textit {\_a}}\right ) {\mathrm e}^{-6 \textit {\_a}}}\, {\mathrm e}^{2 \textit {\_a}}+9\right ) {\mathrm e}^{-2 \textit {\_a}}\right )}^{\frac {1}{3}}}{3 \,{\mathrm e}^{2 \textit {\_a}} 2^{\frac {1}{3}} 3^{\frac {2}{3}} {\left (\left (\sqrt {3}\, \sqrt {\left (4+27 \,{\mathrm e}^{2 \textit {\_a}}\right ) {\mathrm e}^{-6 \textit {\_a}}}\, {\mathrm e}^{2 \textit {\_a}}+9\right ) {\mathrm e}^{-2 \textit {\_a}}\right )}^{\frac {1}{3}}-2 {\left (\left (\sqrt {3}\, \sqrt {\left (4+27 \,{\mathrm e}^{2 \textit {\_a}}\right ) {\mathrm e}^{-6 \textit {\_a}}}\, {\mathrm e}^{2 \textit {\_a}}+9\right ) {\mathrm e}^{-2 \textit {\_a}}\right )}^{\frac {2}{3}} {\mathrm e}^{2 \textit {\_a}}+2 \,2^{\frac {2}{3}} 3^{\frac {1}{3}}}d \textit {\_a} \right )-c_{1} \right ) \\ y \left (x \right ) &= \frac {3 x}{2}+\operatorname {RootOf}\left (-2 \left (\int _{}^{\textit {\_Z}}\frac {{\mathrm e}^{2 \textit {\_a} +3} \left (2 \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+6 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}}}{3 \,{\mathrm e}^{2 \textit {\_a} +3} \left (2 \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+6 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}} 3^{\frac {5}{6}}+4 \,{\mathrm e}^{2 \textit {\_a} +3} 3^{\frac {1}{3}} {\left (\left (\sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+3 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{2}\right )}^{\frac {1}{3}}-9 i {\mathrm e}^{2 \textit {\_a} +3} 3^{\frac {1}{3}} \left (2 \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+6 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}}+2 \,2^{\frac {2}{3}} 3^{\frac {1}{3}} {\mathrm e}^{3}+2 i 2^{\frac {2}{3}} 3^{\frac {5}{6}} {\mathrm e}^{3}}d \textit {\_a} \right ) 3^{\frac {5}{6}}+6 i 3^{\frac {1}{3}} \left (\int _{}^{\textit {\_Z}}\frac {{\mathrm e}^{2 \textit {\_a} +3} \left (2 \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+6 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}}}{3 \,{\mathrm e}^{2 \textit {\_a} +3} \left (2 \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+6 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}} 3^{\frac {5}{6}}+4 \,{\mathrm e}^{2 \textit {\_a} +3} 3^{\frac {1}{3}} {\left (\left (\sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+3 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{2}\right )}^{\frac {1}{3}}-9 i {\mathrm e}^{2 \textit {\_a} +3} 3^{\frac {1}{3}} \left (2 \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+6 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}}+2 \,2^{\frac {2}{3}} 3^{\frac {1}{3}} {\mathrm e}^{3}+2 i 2^{\frac {2}{3}} 3^{\frac {5}{6}} {\mathrm e}^{3}}d \textit {\_a} \right )+c_{1} -x \right ) \\ y \left (x \right ) &= \frac {3 x}{2}+\operatorname {RootOf}\left (2 \left (\int _{}^{\textit {\_Z}}\frac {{\mathrm e}^{2 \textit {\_a} +3} \left (2 \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+6 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}}}{-4 \,{\mathrm e}^{2 \textit {\_a} +3} 3^{\frac {1}{3}} {\left (\left (\sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+3 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{2}\right )}^{\frac {1}{3}}-9 i {\mathrm e}^{2 \textit {\_a} +3} 3^{\frac {1}{3}} \left (2 \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+6 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}}-3 \,{\mathrm e}^{2 \textit {\_a} +3} \left (2 \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+6 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}} 3^{\frac {5}{6}}+2 i 2^{\frac {2}{3}} 3^{\frac {5}{6}} {\mathrm e}^{3}-2 \,2^{\frac {2}{3}} 3^{\frac {1}{3}} {\mathrm e}^{3}}d \textit {\_a} \right ) 3^{\frac {5}{6}}+6 i 3^{\frac {1}{3}} \left (\int _{}^{\textit {\_Z}}\frac {{\mathrm e}^{2 \textit {\_a} +3} \left (2 \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+6 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}}}{-4 \,{\mathrm e}^{2 \textit {\_a} +3} 3^{\frac {1}{3}} {\left (\left (\sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+3 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{2}\right )}^{\frac {1}{3}}-9 i {\mathrm e}^{2 \textit {\_a} +3} 3^{\frac {1}{3}} \left (2 \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+6 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}}-3 \,{\mathrm e}^{2 \textit {\_a} +3} \left (2 \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+6 \sqrt {3}\, {\mathrm e}^{-2 \textit {\_a}}\right )^{\frac {1}{3}} 3^{\frac {5}{6}}+2 i 2^{\frac {2}{3}} 3^{\frac {5}{6}} {\mathrm e}^{3}-2 \,2^{\frac {2}{3}} 3^{\frac {1}{3}} {\mathrm e}^{3}}d \textit {\_a} \right )+c_{1} -x \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