58.2.3 problem 2(b)

Internal problem ID [14544]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, section 1.3. Exercises page 22
Problem number : 2(b)
Date solved : Thursday, October 02, 2025 at 09:38:29 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (-1\right )&={\mathrm e}+3 \\ \end{align*}

✓ Maple. Time used: 0.044 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to e^{-x-1} \left (e x^2+3\right ) \end{align*}

✓ Sympy. Time used: 0.091 (sec). Leaf size: 14

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

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