89.10.16 problem 16

Internal problem ID [24509]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 77
Problem number : 16
Date solved : Thursday, October 02, 2025 at 10:43:57 PM
CAS classification : [[_linear, `class A`]]

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

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

ode:=diff(y(x),x) = x-y(x)+2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 16

ode=D[y[x],x]==x-y[x]+2; 
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: 0.065 (sec). Leaf size: 10

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

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