8.2.5 problem 5

Internal problem ID [665]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.3. Slope fields and solution curves. Page 26
Problem number : 5
Date solved : Tuesday, March 04, 2025 at 11:31:14 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=1-x +y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

ode:=diff(y(x),x) = 1-x+y(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 13

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

\[ y(x)\to x+c_1 e^x \]

✓ Sympy. Time used: 0.111 (sec). Leaf size: 8

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

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