29.34.22 problem 1024

Internal problem ID [5593]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 34
Problem number : 1024
Date solved : Monday, January 27, 2025 at 12:13:03 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3}+y^{\prime }&={\mathrm e}^{y} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 227

dsolve(diff(y(x),x)^3+diff(y(x),x) = exp(y(x)),y(x), singsol=all)
 

\begin{align*} x -6 \left (\int _{}^{y \left (x \right )}\frac {\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{{1}/{3}}}{\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{{2}/{3}}-12}d \textit {\_a} \right )-c_{1} &= 0 \\ \frac {-12 \left (\int _{}^{y \left (x \right )}\frac {\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{{1}/{3}}}{-6-6 i \sqrt {3}-\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{{2}/{3}}}d \textit {\_a} \right )+i \left (-c_{1} +x \right ) \sqrt {3}+x -c_{1}}{1+i \sqrt {3}} &= 0 \\ \frac {12 \left (\int _{}^{y \left (x \right )}\frac {\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{{1}/{3}}}{-\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{{2}/{3}}+\left (\sqrt {3}+3 i\right )^{2}}d \textit {\_a} \right )+i \left (-c_{1} +x \right ) \sqrt {3}+c_{1} -x}{i \sqrt {3}-1} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 174.284 (sec). Leaf size: 1872

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

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