87.11.9 problem 9
Internal
problem
ID
[23427]
Book
:
Ordinary
differential
equations
with
modern
applications.
Ladas,
G.
E.
and
Finizio,
N.
Wadsworth
Publishing.
California.
1978.
ISBN
0-534-00552-7.
QA372.F56
Section
:
Chapter
2.
Linear
differential
equations.
Exercise
at
page
84
Problem
number
:
9
Date
solved
:
Thursday, October 02, 2025 at 09:41:38 PM
CAS
classification
:
[[_high_order, _missing_x]]
\begin{align*} 3 y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.005 (sec). Leaf size: 154
ode:=3*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-2*diff(diff(diff(diff(y(x),x),x),x),x)+diff(diff(y(x),x),x)-2*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = c_2 \,{\mathrm e}^{x}+c_3 \,{\mathrm e}^{-\frac {\left (\left (1844+36 \sqrt {2649}\right )^{{2}/{3}}+2 \left (1844+36 \sqrt {2649}\right )^{{1}/{3}}-32\right ) x}{18 \left (1844+36 \sqrt {2649}\right )^{{1}/{3}}}}+c_1 +{\mathrm e}^{\frac {\left (\left (1844+36 \sqrt {2649}\right )^{{1}/{3}}+4\right ) \left (\left (1844+36 \sqrt {2649}\right )^{{1}/{3}}-8\right ) x}{36 \left (1844+36 \sqrt {2649}\right )^{{1}/{3}}}} \left (\sin \left (\frac {\sqrt {3}\, \left (\left (1844+36 \sqrt {3}\, \sqrt {883}\right )^{{2}/{3}}+32\right ) x}{36 \left (1844+36 \sqrt {3}\, \sqrt {883}\right )^{{1}/{3}}}\right ) c_4 +\cos \left (\frac {\sqrt {3}\, \left (\left (1844+36 \sqrt {3}\, \sqrt {883}\right )^{{2}/{3}}+32\right ) x}{36 \left (1844+36 \sqrt {3}\, \sqrt {883}\right )^{{1}/{3}}}\right ) c_5 \right )
\]
✓ Mathematica. Time used: 0.025 (sec). Leaf size: 149
ode=3*D[y[x],{x,5}]-2*D[y[x],{x,4}]+D[y[x],{x,2}]-2*D[y[x],{x,1}]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \frac {c_3 \exp \left (x \text {Root}\left [3 \text {$\#$1}^3+\text {$\#$1}^2+\text {$\#$1}+2\&,3\right ]\right )}{\text {Root}\left [3 \text {$\#$1}^3+\text {$\#$1}^2+\text {$\#$1}+2\&,3\right ]}+\frac {c_2 \exp \left (x \text {Root}\left [3 \text {$\#$1}^3+\text {$\#$1}^2+\text {$\#$1}+2\&,2\right ]\right )}{\text {Root}\left [3 \text {$\#$1}^3+\text {$\#$1}^2+\text {$\#$1}+2\&,2\right ]}+\frac {c_1 \exp \left (x \text {Root}\left [3 \text {$\#$1}^3+\text {$\#$1}^2+\text {$\#$1}+2\&,1\right ]\right )}{\text {Root}\left [3 \text {$\#$1}^3+\text {$\#$1}^2+\text {$\#$1}+2\&,1\right ]}+c_4 e^x+c_5 \end{align*}
✓ Sympy. Time used: 0.377 (sec). Leaf size: 233
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-2*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 2*Derivative(y(x), (x, 4)) + 3*Derivative(y(x), (x, 5)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{1} + C_{2} e^{\frac {x \left (-4 - \frac {16 \sqrt [3]{2}}{\sqrt [3]{461 + 9 \sqrt {2649}}} + 2^{\frac {2}{3}} \sqrt [3]{461 + 9 \sqrt {2649}}\right )}{36}} \sin {\left (\frac {\sqrt [3]{2} \sqrt {3} x \left (\frac {16}{\sqrt [3]{461 + 9 \sqrt {2649}}} + \sqrt [3]{2} \sqrt [3]{461 + 9 \sqrt {2649}}\right )}{36} \right )} + C_{3} e^{\frac {x \left (-4 - \frac {16 \sqrt [3]{2}}{\sqrt [3]{461 + 9 \sqrt {2649}}} + 2^{\frac {2}{3}} \sqrt [3]{461 + 9 \sqrt {2649}}\right )}{36}} \cos {\left (\frac {\sqrt [3]{2} \sqrt {3} x \left (\frac {16}{\sqrt [3]{461 + 9 \sqrt {2649}}} + \sqrt [3]{2} \sqrt [3]{461 + 9 \sqrt {2649}}\right )}{36} \right )} + C_{4} e^{x} + C_{5} e^{\frac {x \left (- 2^{\frac {2}{3}} \sqrt [3]{461 + 9 \sqrt {2649}} - 2 + \frac {16 \sqrt [3]{2}}{\sqrt [3]{461 + 9 \sqrt {2649}}}\right )}{18}}
\]