23.5.39 problem 39
Internal
problem
ID
[6648]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Part
II.
Chapter
5.
THE
EQUATION
IS
LINEAR
AND
OF
ORDER
GREATER
THAN
TWO,
page
410
Problem
number
:
39
Date
solved
:
Tuesday, September 30, 2025 at 03:50:30 PM
CAS
classification
:
[[_3rd_order, _missing_x]]
\begin{align*} 10 y+3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 149
ode:=10*y(x)+3*diff(y(x),x)-2*diff(diff(y(x),x),x)+diff(diff(diff(y(x),x),x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = {\mathrm e}^{\frac {\left (\left (154+3 \sqrt {2649}\right )^{{1}/{3}}+5\right ) \left (\left (154+3 \sqrt {2649}\right )^{{1}/{3}}-1\right ) x}{6 \left (154+3 \sqrt {2649}\right )^{{1}/{3}}}} \left (\sin \left (\frac {\sqrt {3}\, \left (\left (154+3 \sqrt {3}\, \sqrt {883}\right )^{{2}/{3}}+5\right ) x}{6 \left (154+3 \sqrt {3}\, \sqrt {883}\right )^{{1}/{3}}}\right ) c_2 +\cos \left (\frac {\sqrt {3}\, \left (\left (154+3 \sqrt {3}\, \sqrt {883}\right )^{{2}/{3}}+5\right ) x}{6 \left (154+3 \sqrt {3}\, \sqrt {883}\right )^{{1}/{3}}}\right ) c_3 \right )+c_1 \,{\mathrm e}^{-\frac {\left (\left (154+3 \sqrt {2649}\right )^{{2}/{3}}-2 \left (154+3 \sqrt {2649}\right )^{{1}/{3}}-5\right ) x}{3 \left (154+3 \sqrt {2649}\right )^{{1}/{3}}}}
\]
✓ Mathematica. Time used: 0.002 (sec). Leaf size: 87
ode=10*y[x] + 3*D[y[x],x] - 2*D[y[x],{x,2}] + D[y[x],{x,3}] == 0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}+10\&,1\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}+10\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}+10\&,3\right ]\right ) \end{align*}
✓ Sympy. Time used: 0.304 (sec). Leaf size: 175
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(10*y(x) + 3*Derivative(y(x), x) - 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{1} e^{\frac {x \left (- \frac {5}{\sqrt [3]{154 + 3 \sqrt {2649}}} + 4 + \sqrt [3]{154 + 3 \sqrt {2649}}\right )}{6}} \sin {\left (\frac {\sqrt {3} x \left (\frac {5}{\sqrt [3]{154 + 3 \sqrt {2649}}} + \sqrt [3]{154 + 3 \sqrt {2649}}\right )}{6} \right )} + C_{2} e^{\frac {x \left (- \frac {5}{\sqrt [3]{154 + 3 \sqrt {2649}}} + 4 + \sqrt [3]{154 + 3 \sqrt {2649}}\right )}{6}} \cos {\left (\frac {\sqrt {3} x \left (\frac {5}{\sqrt [3]{154 + 3 \sqrt {2649}}} + \sqrt [3]{154 + 3 \sqrt {2649}}\right )}{6} \right )} + C_{3} e^{\frac {x \left (- \sqrt [3]{154 + 3 \sqrt {2649}} + \frac {5}{\sqrt [3]{154 + 3 \sqrt {2649}}} + 2\right )}{3}}
\]