12.18.6 problem section 9.2, problem 6

Internal problem ID [2120]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 6
Date solved : Tuesday, March 04, 2025 at 01:50:32 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=4*diff(diff(diff(y(x),x),x),x)-8*diff(diff(y(x),x),x)+5*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x c_3 +c_2 \right ) {\mathrm e}^{\frac {x}{2}}+{\mathrm e}^{x} c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 30

ode=4*D[y[x],{x,3}]-8*D[y[x],{x,2}]+5*D[y[x],x]-y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{x/2} \left (c_2 x+c_3 e^{x/2}+c_1\right ) \]

✓ Sympy. Time used: 0.170 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + 5*Derivative(y(x), x) - 8*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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