29.34.21 problem 1023
Internal
problem
ID
[5592]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
34
Problem
number
:
1023
Date
solved
:
Sunday, March 30, 2025 at 09:05:29 AM
CAS
classification
:
[_quadrature]
\begin{align*} {y^{\prime }}^{3}+y^{\prime }-y&=0 \end{align*}
✓ Maple. Time used: 0.035 (sec). Leaf size: 210
ode:=diff(y(x),x)^3+diff(y(x),x)-y(x) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
x -6 \int _{}^{y}\frac {\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{{1}/{3}}}{\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{{2}/{3}}-12}d \textit {\_a} -c_1 &= 0 \\
\frac {12 \int _{}^{y}\frac {\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{{1}/{3}}}{\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\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 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{{1}/{3}}}{\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\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: 0.534 (sec). Leaf size: 335
ode=(D[y[x],x])^3 +D[y[x],x]-y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}}}{2^{2/3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}-6 \sqrt [3]{2}}d\text {$\#$1}\&\right ]\left [-\frac {x}{6}+c_1\right ] \\
y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}}}{-i 2^{2/3} \sqrt {3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}+2^{2/3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}-6 i \sqrt [3]{2} \sqrt {3}-6 \sqrt [3]{2}}d\text {$\#$1}\&\right ]\left [\frac {x}{12}+c_1\right ] \\
y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}}}{i 2^{2/3} \sqrt {3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}+2^{2/3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}+6 i \sqrt [3]{2} \sqrt {3}-6 \sqrt [3]{2}}d\text {$\#$1}\&\right ]\left [\frac {x}{12}+c_1\right ] \\
y(x)\to 0 \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-y(x) + Derivative(y(x), x)**3 + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out