87.11.1 problem 1
Internal
problem
ID
[23419]
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
:
1
Date
solved
:
Thursday, October 02, 2025 at 09:41:35 PM
CAS
classification
:
[[_3rd_order, _missing_x]]
\begin{align*} 4 y^{\prime \prime \prime }-2 y^{\prime \prime }+6 y^{\prime }-7 y&=0 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 148
ode:=4*diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)+6*diff(y(x),x)-7*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = {\mathrm e}^{-\frac {\left (-17+\left (163+3 \sqrt {3498}\right )^{{2}/{3}}-2 \left (163+3 \sqrt {3498}\right )^{{1}/{3}}\right ) x}{12 \left (163+3 \sqrt {3498}\right )^{{1}/{3}}}} \left (-\sin \left (\frac {\sqrt {3}\, \left (\left (163+3 \sqrt {3}\, \sqrt {1166}\right )^{{2}/{3}}+17\right ) x}{12 \left (163+3 \sqrt {3}\, \sqrt {1166}\right )^{{1}/{3}}}\right ) c_2 +\cos \left (\frac {\sqrt {3}\, \left (\left (163+3 \sqrt {3}\, \sqrt {1166}\right )^{{2}/{3}}+17\right ) x}{12 \left (163+3 \sqrt {3}\, \sqrt {1166}\right )^{{1}/{3}}}\right ) c_3 \right )+c_1 \,{\mathrm e}^{\frac {\left (\left (163+3 \sqrt {3498}\right )^{{2}/{3}}+\left (163+3 \sqrt {3498}\right )^{{1}/{3}}-17\right ) x}{6 \left (163+3 \sqrt {3498}\right )^{{1}/{3}}}}
\]
✓ Mathematica. Time used: 0.003 (sec). Leaf size: 93
ode=4*D[y[x],{x,3}]-2*D[y[x],{x,2}]+6*D[y[x],{x,1}]-7*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 [4 \text {$\#$1}^3-2 \text {$\#$1}^2+6 \text {$\#$1}-7\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [4 \text {$\#$1}^3-2 \text {$\#$1}^2+6 \text {$\#$1}-7\&,3\right ]\right )+c_1 \exp \left (x \text {Root}\left [4 \text {$\#$1}^3-2 \text {$\#$1}^2+6 \text {$\#$1}-7\&,1\right ]\right ) \end{align*}
✓ Sympy. Time used: 0.346 (sec). Leaf size: 175
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-7*y(x) + 4*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 3)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{1} e^{- \frac {x \left (\frac {4}{\sqrt [3]{3 \sqrt {3633} + 181}} + 4 + \sqrt [3]{3 \sqrt {3633} + 181}\right )}{12}} \sin {\left (\frac {\sqrt {3} x \left (- \sqrt [3]{3 \sqrt {3633} + 181} + \frac {4}{\sqrt [3]{3 \sqrt {3633} + 181}}\right )}{12} \right )} + C_{2} e^{- \frac {x \left (\frac {4}{\sqrt [3]{3 \sqrt {3633} + 181}} + 4 + \sqrt [3]{3 \sqrt {3633} + 181}\right )}{12}} \cos {\left (\frac {\sqrt {3} x \left (- \sqrt [3]{3 \sqrt {3633} + 181} + \frac {4}{\sqrt [3]{3 \sqrt {3633} + 181}}\right )}{12} \right )} + C_{3} e^{\frac {x \left (-2 + \frac {4}{\sqrt [3]{3 \sqrt {3633} + 181}} + \sqrt [3]{3 \sqrt {3633} + 181}\right )}{6}}
\]