23.2.264 problem 279
Internal
problem
ID
[5619]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Part
II.
Chapter
2.
THE
DIFFERENTIAL
EQUATION
IS
OF
FIRST
ORDER
AND
OF
SECOND
OR
HIGHER
DEGREE,
page
278
Problem
number
:
279
Date
solved
:
Tuesday, September 30, 2025 at 01:13:23 PM
CAS
classification
:
[_quadrature]
\begin{align*} {y^{\prime }}^{3}+y^{\prime }&={\mathrm e}^{y} \end{align*}
✓ Maple. Time used: 0.009 (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}}}{\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}{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: 157.231 (sec). Leaf size: 433
ode=(D[y[x],x])^3 +D[y[x],x]==Exp[ y[x]];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sqrt [3]{\sqrt {3} \sqrt {4+27 e^{2 K[1]}}-9 e^{K[1]}}}{\sqrt [3]{2} \left (\sqrt {3} \sqrt {4+27 e^{2 K[1]}}-9 e^{K[1]}\right )^{2/3}-2 \sqrt [3]{3}}dK[1]\&\right ]\left [-\frac {x}{6^{2/3}}+c_1\right ]\\ y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sqrt [3]{\sqrt {3} \sqrt {4+27 e^{2 K[2]}}-9 e^{K[2]}}}{-i \sqrt [3]{2} 3^{2/3} \left (\sqrt {3} \sqrt {4+27 e^{2 K[2]}}-9 e^{K[2]}\right )^{2/3}+\sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3} \sqrt {4+27 e^{2 K[2]}}-9 e^{K[2]}\right )^{2/3}-2 \sqrt {3}-6 i}dK[2]\&\right ]\left [\frac {x}{2\ 2^{2/3} 3^{5/6}}+c_1\right ]\\ y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sqrt [3]{\sqrt {3} \sqrt {4+27 e^{2 K[3]}}-9 e^{K[3]}}}{i \sqrt [3]{2} 3^{2/3} \left (\sqrt {3} \sqrt {4+27 e^{2 K[3]}}-9 e^{K[3]}\right )^{2/3}+\sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3} \sqrt {4+27 e^{2 K[3]}}-9 e^{K[3]}\right )^{2/3}-2 \sqrt {3}+6 i}dK[3]\&\right ]\left [\frac {x}{2\ 2^{2/3} 3^{5/6}}+c_1\right ] \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