26.7.20 problem Exercise 20.21, page 220

Internal problem ID [7070]
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 20.21, page 220
Date solved : Tuesday, September 30, 2025 at 04:21:07 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 29

ode:=36*diff(diff(diff(diff(y(x),x),x),x),x)-37*diff(diff(y(x),x),x)+4*diff(y(x),x)+5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\frac {x}{2}}+c_2 \,{\mathrm e}^{-x}+c_3 \,{\mathrm e}^{\frac {5 x}{6}}+c_4 \,{\mathrm e}^{-\frac {x}{3}} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 44

ode=36*D[y[x],{x,4}]-37*D[y[x],{x,2}]+4*D[y[x],x]+5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x} \left (c_1 e^{11 x/6}+c_2 e^{2 x/3}+c_3 e^{3 x/2}+c_4\right ) \end{align*}

✓ Sympy. Time used: 0.116 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) + 4*Derivative(y(x), x) - 37*Derivative(y(x), (x, 2)) + 36*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{- \frac {x}{3}} + C_{3} e^{\frac {x}{2}} + C_{4} e^{\frac {5 x}{6}} \]