85.62.2 problem 4

Internal problem ID [22864]
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 209
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:15:54 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=2 \,{\mathrm e}^{3 x}-4 \,{\mathrm e}^{-5 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 35

ode:=diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)-4*diff(y(x),x)-12*y(x) = 2*exp(3*x)-4*exp(-5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 \,{\mathrm e}^{-5 x}}{21}+\frac {{\mathrm e}^{3 x}}{15}+c_1 \,{\mathrm e}^{-3 x}+c_2 \,{\mathrm e}^{-2 x}+c_3 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.059 (sec). Leaf size: 48

ode=D[y[x],{x,3}]+3*D[y[x],{x,2}]-4*D[y[x],{x,1}]-12*y[x]==2*Exp[3*x]-4*Exp[-5*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 e^{-5 x}}{21}+\frac {e^{3 x}}{15}+c_1 e^{-3 x}+c_2 e^{-2 x}+c_3 e^{2 x} \end{align*}

✓ Sympy. Time used: 0.198 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*y(x) - 2*exp(3*x) - 4*Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) + 4*exp(-5*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 3 x} + C_{2} e^{- 2 x} + C_{3} e^{2 x} + \frac {e^{3 x}}{15} + \frac {2 e^{- 5 x}}{21} \]