29.35.6 problem 1038

Internal problem ID [5604]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1038
Date solved : Monday, January 27, 2025 at 12:13:35 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} {y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 14.010 (sec). Leaf size: 942

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^{{1}/{3}} 3^{{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 )}^{{1}/{3}}}{3 \,{\mathrm e}^{2 \textit {\_a}} 2^{{1}/{3}} 3^{{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 )}^{{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 )}^{{2}/{3}} {\mathrm e}^{2 \textit {\_a}}+2 \,2^{{2}/{3}} 3^{{1}/{3}}}d \textit {\_a} \right )-c_{1} \right ) \\ y \left (x \right ) &= \frac {3 x}{2}+\operatorname {RootOf}\left (6 i 2^{{1}/{3}} 3^{{1}/{6}} \left (\int _{}^{\textit {\_Z}}\frac {{\mathrm e}^{2 \textit {\_a} +3} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{1}/{3}}}{-2 i {\mathrm e}^{3} 2^{{2}/{3}} 3^{{5}/{6}}+9 i {\mathrm e}^{2 \textit {\_a} +3} 2^{{1}/{3}} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{1}/{3}} 3^{{1}/{6}}-4 \,{\mathrm e}^{2 \textit {\_a} +3} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{2}/{3}}-3 \,{\mathrm e}^{2 \textit {\_a} +3} 2^{{1}/{3}} 3^{{2}/{3}} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{1}/{3}}-2 \,2^{{2}/{3}} 3^{{1}/{3}} {\mathrm e}^{3}}d \textit {\_a} \right )-2 \,2^{{1}/{3}} 3^{{2}/{3}} \left (\int _{}^{\textit {\_Z}}\frac {{\mathrm e}^{2 \textit {\_a} +3} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{1}/{3}}}{-2 i {\mathrm e}^{3} 2^{{2}/{3}} 3^{{5}/{6}}+9 i {\mathrm e}^{2 \textit {\_a} +3} 2^{{1}/{3}} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{1}/{3}} 3^{{1}/{6}}-4 \,{\mathrm e}^{2 \textit {\_a} +3} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{2}/{3}}-3 \,{\mathrm e}^{2 \textit {\_a} +3} 2^{{1}/{3}} 3^{{2}/{3}} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{1}/{3}}-2 \,2^{{2}/{3}} 3^{{1}/{3}} {\mathrm e}^{3}}d \textit {\_a} \right )-c_{1} +x \right ) \\ y \left (x \right ) &= \frac {3 x}{2}+\operatorname {RootOf}\left (6 i 2^{{1}/{3}} 3^{{1}/{6}} \left (\int _{}^{\textit {\_Z}}\frac {{\mathrm e}^{2 \textit {\_a} +3} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{1}/{3}}}{-2 i {\mathrm e}^{3} 2^{{2}/{3}} 3^{{5}/{6}}+9 i {\mathrm e}^{2 \textit {\_a} +3} 2^{{1}/{3}} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{1}/{3}} 3^{{1}/{6}}+4 \,{\mathrm e}^{2 \textit {\_a} +3} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{2}/{3}}+3 \,{\mathrm e}^{2 \textit {\_a} +3} 2^{{1}/{3}} 3^{{2}/{3}} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{1}/{3}}+2 \,2^{{2}/{3}} 3^{{1}/{3}} {\mathrm e}^{3}}d \textit {\_a} \right )+2 \,2^{{1}/{3}} 3^{{2}/{3}} \left (\int _{}^{\textit {\_Z}}\frac {{\mathrm e}^{2 \textit {\_a} +3} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{1}/{3}}}{-2 i {\mathrm e}^{3} 2^{{2}/{3}} 3^{{5}/{6}}+9 i {\mathrm e}^{2 \textit {\_a} +3} 2^{{1}/{3}} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{1}/{3}} 3^{{1}/{6}}+4 \,{\mathrm e}^{2 \textit {\_a} +3} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{2}/{3}}+3 \,{\mathrm e}^{2 \textit {\_a} +3} 2^{{1}/{3}} 3^{{2}/{3}} \left (\sqrt {3}\, \sqrt {{\mathrm e}^{-4 \textit {\_a}} \left (4 \,{\mathrm e}^{-2 \textit {\_a}}+27\right )}+9 \,{\mathrm e}^{-2 \textit {\_a}}\right )^{{1}/{3}}+2 \,2^{{2}/{3}} 3^{{1}/{3}} {\mathrm e}^{3}}d \textit {\_a} \right )-c_{1} +x \right ) \\ \end{align*}

✗ Solution by Mathematica

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

DSolve[(D[y[x],x])^3 +Exp[3*x -2*y[x]]*(D[y[x],x]-1)==0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out