89.14.10 problem 10

Internal problem ID [24614]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 128
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:46:30 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime }+28 y^{\prime \prime }+61 y^{\prime }+37 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=4*diff(diff(diff(y(x),x),x),x)+28*diff(diff(y(x),x),x)+61*diff(y(x),x)+37*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 38

ode=4*D[y[x],{x,3}]+28*D[y[x],{x,2}]+61*D[y[x],{x,1}]+37*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x} \left (c_3 e^{2 x}+c_2 \cos \left (\frac {x}{2}\right )+c_1 \sin \left (\frac {x}{2}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.133 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(37*y(x) + 61*Derivative(y(x), x) + 28*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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