23.5.25 problem 25
Internal
problem
ID
[6634]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Part
II.
Chapter
5.
THE
EQUATION
IS
LINEAR
AND
OF
ORDER
GREATER
THAN
TWO,
page
410
Problem
number
:
25
Date
solved
:
Tuesday, September 30, 2025 at 03:50:24 PM
CAS
classification
:
[[_3rd_order, _missing_x]]
\begin{align*} y+y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 149
ode:=y(x)+diff(y(x),x)-diff(diff(y(x),x),x)+diff(diff(diff(y(x),x),x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = {\mathrm e}^{\frac {\left (-2+\left (17+3 \sqrt {33}\right )^{{2}/{3}}+2 \left (17+3 \sqrt {33}\right )^{{1}/{3}}\right ) x}{6 \left (17+3 \sqrt {33}\right )^{{1}/{3}}}} \left (\sin \left (\frac {\sqrt {3}\, \left (\left (17+3 \sqrt {3}\, \sqrt {11}\right )^{{2}/{3}}+2\right ) x}{6 \left (17+3 \sqrt {3}\, \sqrt {11}\right )^{{1}/{3}}}\right ) c_2 +\cos \left (\frac {\sqrt {3}\, \left (\left (17+3 \sqrt {3}\, \sqrt {11}\right )^{{2}/{3}}+2\right ) x}{6 \left (17+3 \sqrt {3}\, \sqrt {11}\right )^{{1}/{3}}}\right ) c_3 \right )+{\mathrm e}^{-\frac {\left (\left (17+3 \sqrt {33}\right )^{{1}/{3}}+1\right ) \left (\left (17+3 \sqrt {33}\right )^{{1}/{3}}-2\right ) x}{3 \left (17+3 \sqrt {33}\right )^{{1}/{3}}}} c_1
\]
✓ Mathematica. Time used: 0.002 (sec). Leaf size: 81
ode=y[x] + D[y[x],x] - D[y[x],{x,2}] + D[y[x],{x,3}] == 0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2+\text {$\#$1}+1\&,1\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2+\text {$\#$1}+1\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2+\text {$\#$1}+1\&,3\right ]\right ) \end{align*}
✓ Sympy. Time used: 0.244 (sec). Leaf size: 175
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(y(x) + Derivative(y(x), x) - Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{1} e^{\frac {x \left (- \frac {2}{\sqrt [3]{17 + 3 \sqrt {33}}} + 2 + \sqrt [3]{17 + 3 \sqrt {33}}\right )}{6}} \sin {\left (\frac {\sqrt {3} x \left (\frac {2}{\sqrt [3]{17 + 3 \sqrt {33}}} + \sqrt [3]{17 + 3 \sqrt {33}}\right )}{6} \right )} + C_{2} e^{\frac {x \left (- \frac {2}{\sqrt [3]{17 + 3 \sqrt {33}}} + 2 + \sqrt [3]{17 + 3 \sqrt {33}}\right )}{6}} \cos {\left (\frac {\sqrt {3} x \left (\frac {2}{\sqrt [3]{17 + 3 \sqrt {33}}} + \sqrt [3]{17 + 3 \sqrt {33}}\right )}{6} \right )} + C_{3} e^{\frac {x \left (- \sqrt [3]{17 + 3 \sqrt {33}} + \frac {2}{\sqrt [3]{17 + 3 \sqrt {33}}} + 1\right )}{3}}
\]