32.8.25 problem Exercise 21.33, page 231

Internal problem ID [5974]
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 21.33, page 231
Date solved : Wednesday, March 05, 2025 at 12:01:18 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = exp(-x); 
ic:=y(0) = 1, D(y)(0) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y \left (x \right ) = -\frac {5 \,{\mathrm e}^{2 x}}{3}+\frac {5 \,{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{6} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 31

ode=D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==Exp[-x]; 
ic={y[0]==1,Derivative[1][y][0] ==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^{-x}}{6}+\frac {5 e^x}{2}-\frac {5 e^{2 x}}{3} \]

✓ Sympy. Time used: 0.215 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - exp(-x),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {5 e^{2 x}}{3} + \frac {5 e^{x}}{2} + \frac {e^{- x}}{6} \]