26.7.19 problem Exercise 20.20, page 220

Internal problem ID [7069]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20.20, page 220
Date solved : Tuesday, September 30, 2025 at 04:21:06 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(diff(y(x),x),x),x)-11*diff(diff(y(x),x),x)-12*diff(y(x),x)+36*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-3 x} \left (\left (c_2 x +c_1 \right ) {\mathrm e}^{5 x}+c_4 x +c_3 \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 35

ode=D[y[x],{x,4}]+2*D[y[x],{x,3}]-11*D[y[x],{x,2}]-12*D[y[x],x]+36*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x} \left (c_3 e^{5 x}+x \left (c_4 e^{5 x}+c_2\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*y(x) - 12*Derivative(y(x), x) - 11*Derivative(y(x), (x, 2)) + 2*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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