87.11.5 problem 5
Internal
problem
ID
[23423]
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
:
5
Date
solved
:
Thursday, October 02, 2025 at 09:41:37 PM
CAS
classification
:
[[_3rd_order, _missing_x]]
\begin{align*} 5 y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-2 y&=0 \end{align*}
✓ Maple. Time used: 0.002 (sec). Leaf size: 138
ode:=5*diff(diff(diff(y(x),x),x),x)-5*diff(diff(y(x),x),x)+diff(y(x),x)-2*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \left (c_1 \,{\mathrm e}^{\frac {x \left (40+\left (5500+60 \sqrt {8385}\right )^{{2}/{3}}\right )}{20 \left (5500+60 \sqrt {8385}\right )^{{1}/{3}}}}-c_2 \sin \left (\frac {\sqrt {3}\, \left (\left (5500+60 \sqrt {3}\, \sqrt {2795}\right )^{{2}/{3}}-40\right ) x}{60 \left (5500+60 \sqrt {3}\, \sqrt {2795}\right )^{{1}/{3}}}\right )+c_3 \cos \left (\frac {\sqrt {3}\, \left (\left (5500+60 \sqrt {3}\, \sqrt {2795}\right )^{{2}/{3}}-40\right ) x}{60 \left (5500+60 \sqrt {3}\, \sqrt {2795}\right )^{{1}/{3}}}\right )\right ) {\mathrm e}^{-\frac {\left (40+\left (5500+60 \sqrt {8385}\right )^{{2}/{3}}-20 \left (5500+60 \sqrt {8385}\right )^{{1}/{3}}\right ) x}{60 \left (5500+60 \sqrt {8385}\right )^{{1}/{3}}}}
\]
✓ Mathematica. Time used: 0.002 (sec). Leaf size: 87
ode=5*D[y[x],{x,3}]-5*D[y[x],{x,2}]+D[y[x],{x,1}]+2*y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to c_1 \exp \left (x \text {Root}\left [5 \text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}+2\&,1\right ]\right )+c_2 \exp \left (x \text {Root}\left [5 \text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}+2\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [5 \text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}+2\&,3\right ]\right ) \end{align*}
✓ Sympy. Time used: 0.293 (sec). Leaf size: 226
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(2*y(x) + Derivative(y(x), x) - 5*Derivative(y(x), (x, 2)) + 5*Derivative(y(x), (x, 3)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{1} e^{\frac {x \left (\frac {4 \sqrt [3]{50}}{\sqrt [3]{9 \sqrt {865} + 265}} + 20 + \sqrt [3]{20} \sqrt [3]{9 \sqrt {865} + 265}\right )}{60}} \sin {\left (\frac {\sqrt {3} x \left (- \sqrt [3]{20} \sqrt [3]{9 \sqrt {865} + 265} + \frac {4 \sqrt [3]{50}}{\sqrt [3]{9 \sqrt {865} + 265}}\right )}{60} \right )} + C_{2} e^{\frac {x \left (\frac {4 \sqrt [3]{50}}{\sqrt [3]{9 \sqrt {865} + 265}} + 20 + \sqrt [3]{20} \sqrt [3]{9 \sqrt {865} + 265}\right )}{60}} \cos {\left (\frac {\sqrt {3} x \left (- \sqrt [3]{20} \sqrt [3]{9 \sqrt {865} + 265} + \frac {4 \sqrt [3]{50}}{\sqrt [3]{9 \sqrt {865} + 265}}\right )}{60} \right )} + C_{3} e^{\frac {x \left (- \sqrt [3]{20} \sqrt [3]{9 \sqrt {865} + 265} - \frac {4 \sqrt [3]{50}}{\sqrt [3]{9 \sqrt {865} + 265}} + 10\right )}{30}}
\]