11.1.7 problem 16
Internal
problem
ID
[1468]
Book
:
Elementary
differential
equations
and
boundary
value
problems,
11th
ed.,
Boyce,
DiPrima,
Meade
Section
:
Chapter
4.1,
Higher
order
linear
differential
equations.
General
theory.
page
173
Problem
number
:
16
Date
solved
:
Saturday, March 29, 2025 at 10:55:56 PM
CAS
classification
:
[[_3rd_order, _missing_x]]
\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-3 y&=0 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 138
ode:=diff(diff(diff(y(x),x),x),x)+2*diff(diff(y(x),x),x)-diff(y(x),x)-3*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \left (c_1 \,{\mathrm e}^{\frac {x \left (28+\left (188+12 \sqrt {93}\right )^{{2}/{3}}\right )}{4 \left (188+12 \sqrt {93}\right )^{{1}/{3}}}}-c_2 \sin \left (\frac {\sqrt {3}\, \left (\left (188+12 \sqrt {3}\, \sqrt {31}\right )^{{2}/{3}}-28\right ) x}{12 \left (188+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}}}\right )+c_3 \cos \left (\frac {\sqrt {3}\, \left (\left (188+12 \sqrt {3}\, \sqrt {31}\right )^{{2}/{3}}-28\right ) x}{12 \left (188+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}}}\right )\right ) {\mathrm e}^{-\frac {\left (28+\left (188+12 \sqrt {93}\right )^{{2}/{3}}+8 \left (188+12 \sqrt {93}\right )^{{1}/{3}}\right ) x}{12 \left (188+12 \sqrt {93}\right )^{{1}/{3}}}}
\]
✓ Mathematica. Time used: 0.003 (sec). Leaf size: 87
ode=D[y[x],{x,3}]+2*D[y[x],{x,2}]-D[y[x],x]-3*y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
y(x)\to c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-3\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-3\&,3\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}-3\&,1\right ]\right )
\]
✓ Sympy. Time used: 0.541 (sec). Leaf size: 226
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-3*y(x) - Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{1} e^{- \frac {x \left (\frac {14 \sqrt [3]{2}}{\sqrt [3]{3 \sqrt {93} + 47}} + 2^{\frac {2}{3}} \sqrt [3]{3 \sqrt {93} + 47} + 8\right )}{12}} \sin {\left (\frac {\sqrt [3]{2} \sqrt {3} x \left (- \sqrt [3]{2} \sqrt [3]{3 \sqrt {93} + 47} + \frac {14}{\sqrt [3]{3 \sqrt {93} + 47}}\right )}{12} \right )} + C_{2} e^{- \frac {x \left (\frac {14 \sqrt [3]{2}}{\sqrt [3]{3 \sqrt {93} + 47}} + 2^{\frac {2}{3}} \sqrt [3]{3 \sqrt {93} + 47} + 8\right )}{12}} \cos {\left (\frac {\sqrt [3]{2} \sqrt {3} x \left (- \sqrt [3]{2} \sqrt [3]{3 \sqrt {93} + 47} + \frac {14}{\sqrt [3]{3 \sqrt {93} + 47}}\right )}{12} \right )} + C_{3} e^{\frac {x \left (-4 + \frac {14 \sqrt [3]{2}}{\sqrt [3]{3 \sqrt {93} + 47}} + 2^{\frac {2}{3}} \sqrt [3]{3 \sqrt {93} + 47}\right )}{6}}
\]