81.6.7 problem 7-7

Internal problem ID [21553]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 7. Linear Differential Equations. Page 101.
Problem number : 7-7
Date solved : Thursday, October 02, 2025 at 07:48:01 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = x -1+{\mathrm e}^{-x} c_1 \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.072 (sec). Leaf size: 10

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

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