77.19.7 problem 7

Internal problem ID [20520]
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 : Thursday, October 02, 2025 at 06:04:09 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 222

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

\begin{align*} x -6 \int _{}^{y}\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} -c_1 &= 0 \\ \frac {12 \int _{}^{y}\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} +i \left (x -c_1 \right ) \sqrt {3}+x -c_1}{1+i \sqrt {3}} &= 0 \\ \frac {-12 \int _{}^{y}\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} +i \left (x -c_1 \right ) \sqrt {3}-x +c_1}{i \sqrt {3}-1} &= 0 \\ \end{align*}

✓ Mathematica. Time used: 140.22 (sec). Leaf size: 1244

ode=D[y[x],x]^3+D[y[x],x]==Exp[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(y(x)) + Derivative(y(x), x)**3 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out