14.7.4 problem Problem 28

Internal problem ID [3719]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.3, The Method of Undetermined Coefficients. page 525
Problem number : Problem 28
Date solved : Tuesday, September 30, 2025 at 06:56:20 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to c_1 e^{-x}+e^{2 x} \left (\frac {5 x}{3}-\frac {5}{9}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.126 (sec). Leaf size: 19

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

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