89.16.7 problem 7

Internal problem ID [24657]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 9. Nonhomogeneous Equations: Undetermined coefficients. Exercises at page 140
Problem number : 7
Date solved : Thursday, October 02, 2025 at 10:46:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

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

\[ y = \left (3 \,{\mathrm e}^{4 x}+c_2 \,{\mathrm e}^{3 x}+c_1 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 0.100 (sec). Leaf size: 20

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

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