83.19.7 problem 7

Internal problem ID [19235]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (B) at page 55
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 01:15:13 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.012 (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}}}{-\left (108 \,{\mathrm e}^{\textit {\_a}}+12 \sqrt {12+81 \,{\mathrm e}^{2 \textit {\_a}}}\right )^{{2}/{3}}-6-6 i \sqrt {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}-x +c_{1}}{i \sqrt {3}-1} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 162.396 (sec). Leaf size: 1872

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

Too large to display