87.11.2 problem 2
Internal
problem
ID
[23420]
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
:
2
Date
solved
:
Thursday, October 02, 2025 at 09:41:36 PM
CAS
classification
:
[[_high_order, _missing_x]]
\begin{align*} 2 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-y&=0 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 39
ode:=2*diff(diff(diff(diff(y(x),x),x),x),x)+3*diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)+2*diff(y(x),x)-y(x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (2 \textit {\_Z}^{4}+3 \textit {\_Z}^{3}-\textit {\_Z}^{2}+2 \textit {\_Z} -1, \operatorname {index} =\textit {\_a} \right ) x} \textit {\_C}_{\textit {\_a}}
\]
✓ Mathematica. Time used: 0.003 (sec). Leaf size: 146
ode=2*D[y[x],{x,4}]+3*D[y[x],{x,3}]-D[y[x],{x,2}]+2*D[y[x],{x,1}]-y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to c_3 \exp \left (x \text {Root}\left [2 \text {$\#$1}^4+3 \text {$\#$1}^3-\text {$\#$1}^2+2 \text {$\#$1}-1\&,3\right ]\right )+c_4 \exp \left (x \text {Root}\left [2 \text {$\#$1}^4+3 \text {$\#$1}^3-\text {$\#$1}^2+2 \text {$\#$1}-1\&,4\right ]\right )+c_2 \exp \left (x \text {Root}\left [2 \text {$\#$1}^4+3 \text {$\#$1}^3-\text {$\#$1}^2+2 \text {$\#$1}-1\&,2\right ]\right )+c_1 \exp \left (x \text {Root}\left [2 \text {$\#$1}^4+3 \text {$\#$1}^3-\text {$\#$1}^2+2 \text {$\#$1}-1\&,1\right ]\right ) \end{align*}
✓ Sympy. Time used: 1.053 (sec). Leaf size: 624
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-y(x) + 2*Derivative(y(x), x) - Derivative(y(x), (x, 2)) + 3*Derivative(y(x), (x, 3)) + 2*Derivative(y(x), (x, 4)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{1} e^{\frac {x \left (-9 + \sqrt {3} \sqrt {- \frac {328 \sqrt [3]{2}}{\sqrt [3]{-119 + 3 \sqrt {32205}}} + 43 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{-119 + 3 \sqrt {32205}}}\right )}{24}} \sin {\left (\frac {\sqrt {6} x \sqrt {-43 - \frac {164 \sqrt [3]{2}}{\sqrt [3]{-119 + 3 \sqrt {32205}}} + 2 \cdot 2^{\frac {2}{3}} \sqrt [3]{-119 + 3 \sqrt {32205}} + \frac {345 \sqrt {3}}{\sqrt {- \frac {328 \sqrt [3]{2}}{\sqrt [3]{-119 + 3 \sqrt {32205}}} + 43 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{-119 + 3 \sqrt {32205}}}}}}{24} \right )} + C_{2} e^{\frac {x \left (-9 + \sqrt {3} \sqrt {- \frac {328 \sqrt [3]{2}}{\sqrt [3]{-119 + 3 \sqrt {32205}}} + 43 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{-119 + 3 \sqrt {32205}}}\right )}{24}} \cos {\left (\frac {\sqrt {6} x \sqrt {-43 - \frac {164 \sqrt [3]{2}}{\sqrt [3]{-119 + 3 \sqrt {32205}}} + 2 \cdot 2^{\frac {2}{3}} \sqrt [3]{-119 + 3 \sqrt {32205}} + \frac {345 \sqrt {3}}{\sqrt {- \frac {328 \sqrt [3]{2}}{\sqrt [3]{-119 + 3 \sqrt {32205}}} + 43 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{-119 + 3 \sqrt {32205}}}}}}{24} \right )} + C_{3} e^{- \frac {x \left (9 + \sqrt {3} \sqrt {- \frac {328 \sqrt [3]{2}}{\sqrt [3]{-119 + 3 \sqrt {32205}}} + 43 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{-119 + 3 \sqrt {32205}}} + \sqrt {6} \sqrt {- 2 \cdot 2^{\frac {2}{3}} \sqrt [3]{-119 + 3 \sqrt {32205}} + \frac {164 \sqrt [3]{2}}{\sqrt [3]{-119 + 3 \sqrt {32205}}} + 43 + \frac {345 \sqrt {3}}{\sqrt {- \frac {328 \sqrt [3]{2}}{\sqrt [3]{-119 + 3 \sqrt {32205}}} + 43 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{-119 + 3 \sqrt {32205}}}}}\right )}{24}} + C_{4} e^{\frac {x \left (- \sqrt {3} \sqrt {- \frac {328 \sqrt [3]{2}}{\sqrt [3]{-119 + 3 \sqrt {32205}}} + 43 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{-119 + 3 \sqrt {32205}}} - 9 + \sqrt {6} \sqrt {- 2 \cdot 2^{\frac {2}{3}} \sqrt [3]{-119 + 3 \sqrt {32205}} + \frac {164 \sqrt [3]{2}}{\sqrt [3]{-119 + 3 \sqrt {32205}}} + 43 + \frac {345 \sqrt {3}}{\sqrt {- \frac {328 \sqrt [3]{2}}{\sqrt [3]{-119 + 3 \sqrt {32205}}} + 43 + 4 \cdot 2^{\frac {2}{3}} \sqrt [3]{-119 + 3 \sqrt {32205}}}}}\right )}{24}}
\]