89.14.5 problem 5

Internal problem ID [24609]
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 : 5
Date solved : Thursday, October 02, 2025 at 10:46:28 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime }+8 y^{\prime \prime }-11 y^{\prime }+3 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=4*diff(diff(diff(y(x),x),x),x)+8*diff(diff(y(x),x),x)-11*diff(y(x),x)+3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 29

ode=4*D[y[x],{x,3}]+8*D[y[x],{x,2}]-11*D[y[x],{x,1}]+3*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x} \left (e^{7 x/2} (c_2 x+c_1)+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.132 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) - 11*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)
 

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