89.12.14 problem 14

Internal problem ID [24568]
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 121
Problem number : 14
Date solved : Thursday, October 02, 2025 at 10:46:09 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }-23 y^{\prime \prime }+12 y^{\prime }+36 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

ode:=4*diff(diff(diff(diff(y(x),x),x),x),x)-4*diff(diff(diff(y(x),x),x),x)-23*diff(diff(y(x),x),x)+12*diff(y(x),x)+36*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 41

ode=4*D[y[x],{x,4}]-4*D[y[x],{x,3}]-23*D[y[x],{x,2}]+12*D[y[x],{x,1}]+ 36*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x/2} \left (c_3 e^{7 x/2}+x \left (c_4 e^{7 x/2}+c_2\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.122 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*y(x) + 12*Derivative(y(x), x) - 23*Derivative(y(x), (x, 2)) - 4*Derivative(y(x), (x, 3)) + 4*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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