1.11.46 problem 48

Internal problem ID [367]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 48
Date solved : Tuesday, September 30, 2025 at 03:57:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to \frac {1}{12} e^{-2 x} \left (-6 x+12 c_2 e^{6 x}-1+12 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.147 (sec). Leaf size: 19

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

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