12.18.13 problem section 9.2, problem 13

Internal problem ID [2127]
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 13
Date solved : Tuesday, March 04, 2025 at 01:50:36 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+3 y^{\prime \prime }-13 y^{\prime }-6 y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 29

ode:=4*diff(diff(diff(diff(y(x),x),x),x),x)+12*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)-13*diff(y(x),x)-6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{3 x}+c_2 \,{\mathrm e}^{\frac {3 x}{2}}+c_4 \,{\mathrm e}^{\frac {x}{2}}+c_3 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 42

ode=4*D[y[x],{x,4}]+12*D[y[x],{x,3}]+3*D[y[x],{x,2}]-13*D[y[x],x]-6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (c_1 e^{x/2}+c_2 e^{3 x/2}+c_4 e^{3 x}+c_3\right ) \]

✓ Sympy. Time used: 0.214 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) - 13*Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)) + 12*Derivative(y(x), (x, 3)) + 4*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{- \frac {3 x}{2}} + C_{3} e^{- \frac {x}{2}} + C_{4} e^{x} \]