73.17.23 problem 23

Internal problem ID [15486]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 23
Date solved : Monday, March 31, 2025 at 01:39:14 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }&=8 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 50

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+12*diff(y(x),x) = 8; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{3 x} \left (-\frac {c_2 \sqrt {3}}{3}+c_1 \right ) \cos \left (\sqrt {3}\, x \right )}{4}+\frac {{\mathrm e}^{3 x} \left (c_1 \sqrt {3}+3 c_2 \right ) \sin \left (\sqrt {3}\, x \right )}{12}+\frac {2 x}{3}+c_3 \]

✓ Mathematica. Time used: 60.045 (sec). Leaf size: 55

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+12*D[y[x],x]==8; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \int _1^x\left (e^{3 K[1]} c_2 \cos \left (\sqrt {3} K[1]\right )+e^{3 K[1]} c_1 \sin \left (\sqrt {3} K[1]\right )+\frac {2}{3}\right )dK[1]+c_3 \]

✓ Sympy. Time used: 0.215 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 8,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {2 x}{3} + \left (C_{2} \sin {\left (\sqrt {3} x \right )} + C_{3} \cos {\left (\sqrt {3} x \right )}\right ) e^{3 x} \]