58.11.2 problem 2

Internal problem ID [14733]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:50:36 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 30

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)-8*y(x) = 4*exp(2*x)-21*exp(-3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (2 \,{\mathrm e}^{7 x} c_2 -{\mathrm e}^{5 x}+2 c_1 \,{\mathrm e}^{x}-6\right ) {\mathrm e}^{-3 x}}{2} \]

✓ Mathematica. Time used: 0.076 (sec). Leaf size: 38

ode=D[y[x],{x,2}]-2*D[y[x],x]-8*y[x]==4*Exp[2*x]-21*Exp[-3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{2} e^{-3 x} \left (e^{5 x}+6\right )+c_1 e^{-2 x}+c_2 e^{4 x} \end{align*}

✓ Sympy. Time used: 0.167 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*y(x) - 4*exp(2*x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + 21*exp(-3*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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