87.16.14 problem 14

Internal problem ID [23583]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 119
Problem number : 14
Date solved : Thursday, October 02, 2025 at 09:43:11 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = -\left (x +c_1 +1\right ) {\mathrm e}^{-x}+c_2 \]

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to c_2-e^{-x} (x+1+c_1) \end{align*}

✓ Sympy. Time used: 0.105 (sec). Leaf size: 10

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

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