85.38.1 problem 1

Internal problem ID [22753]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. B Exercises at page 175
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:14:21 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+2 y^{\prime }-12 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 32

ode:=diff(diff(diff(y(x),x),x),x)+5*diff(diff(y(x),x),x)+2*diff(y(x),x)-12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-3 x}+c_2 \,{\mathrm e}^{\left (\sqrt {5}-1\right ) x}+c_3 \,{\mathrm e}^{-\left (\sqrt {5}+1\right ) x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 43

ode=D[y[x],{x,3}]+5*D[y[x],{x,2}]+2*D[y[x],x]-12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x} \left (c_1 e^{-\left (\left (\sqrt {5}-2\right ) x\right )}+c_2 e^{\left (2+\sqrt {5}\right ) x}+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.143 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*y(x) + 2*Derivative(y(x), x) + 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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