75.3.3 problem 3

Internal problem ID [19907]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 3
Date solved : Thursday, October 02, 2025 at 05:00:48 PM
CAS classification : [[_linear, `class A`]]

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

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

ode:=diff(y(x),x) = x-y(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]==x-y[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: 0.062 (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)
 

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