32.8.1 problem Exercise 21.3, page 231

Internal problem ID [5950]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined Coefficients
Problem number : Exercise 21.3, page 231
Date solved : Tuesday, March 04, 2025 at 11:59:47 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+3*diff(y(x),x)+2*y(x) = 4; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 23

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

\[ y(x)\to c_1 e^{-2 x}+c_2 e^{-x}+2 \]

✓ Sympy. Time used: 0.161 (sec). Leaf size: 15

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

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