87.11.3 problem 3
Internal
problem
ID
[23421]
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
:
3
Date
solved
:
Thursday, October 02, 2025 at 09:41:36 PM
CAS
classification
:
[[_3rd_order, _missing_x]]
\begin{align*} y^{\prime \prime \prime }-y^{\prime }+2 y&=0 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 127
ode:=diff(diff(diff(y(x),x),x),x)-diff(y(x),x)+2*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = {\mathrm e}^{\frac {\left (\left (27+3 \sqrt {78}\right )^{{2}/{3}}+3\right ) x}{6 \left (27+3 \sqrt {78}\right )^{{1}/{3}}}} \left (\sin \left (\frac {\sqrt {3}\, \left (\left (27+3 \sqrt {3}\, \sqrt {26}\right )^{{2}/{3}}-3\right ) x}{6 \left (27+3 \sqrt {3}\, \sqrt {26}\right )^{{1}/{3}}}\right ) c_2 +\cos \left (\frac {\sqrt {3}\, \left (\left (27+3 \sqrt {3}\, \sqrt {26}\right )^{{2}/{3}}-3\right ) x}{6 \left (27+3 \sqrt {3}\, \sqrt {26}\right )^{{1}/{3}}}\right ) c_3 \right )+c_1 \,{\mathrm e}^{-\frac {\left (\left (27+3 \sqrt {78}\right )^{{2}/{3}}+3\right ) x}{3 \left (27+3 \sqrt {78}\right )^{{1}/{3}}}}
\]
✓ Mathematica. Time used: 0.002 (sec). Leaf size: 69
ode=D[y[x],{x,3}]-D[y[x],{x,1}]+2*y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}+2\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}+2\&,3\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}+2\&,1\right ]\right ) \end{align*}
✓ Sympy. Time used: 0.331 (sec). Leaf size: 189
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(2*y(x) - Derivative(y(x), x) + Derivative(y(x), (x, 3)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{1} e^{\frac {\sqrt [3]{3} x \left (\frac {\sqrt [3]{3}}{\sqrt [3]{\sqrt {78} + 9}} + \sqrt [3]{\sqrt {78} + 9}\right )}{6}} \sin {\left (\frac {\sqrt [6]{3} x \left (- 3^{\frac {2}{3}} \sqrt [3]{\sqrt {78} + 9} + \frac {3}{\sqrt [3]{\sqrt {78} + 9}}\right )}{6} \right )} + C_{2} e^{\frac {\sqrt [3]{3} x \left (\frac {\sqrt [3]{3}}{\sqrt [3]{\sqrt {78} + 9}} + \sqrt [3]{\sqrt {78} + 9}\right )}{6}} \cos {\left (\frac {\sqrt [6]{3} x \left (- 3^{\frac {2}{3}} \sqrt [3]{\sqrt {78} + 9} + \frac {3}{\sqrt [3]{\sqrt {78} + 9}}\right )}{6} \right )} + C_{3} e^{- \frac {\sqrt [3]{3} x \left (\frac {\sqrt [3]{3}}{\sqrt [3]{\sqrt {78} + 9}} + \sqrt [3]{\sqrt {78} + 9}\right )}{3}}
\]