26.9.6 problem Exercise 22.6, page 240

Internal problem ID [7115]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number : Exercise 22.6, page 240
Date solved : Tuesday, September 30, 2025 at 04:21:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

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

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

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 0.100 (sec). Leaf size: 19

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

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