50.4.9 problem 9

Internal problem ID [7858]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page 20
Problem number : 9
Date solved : Sunday, March 30, 2025 at 12:31:32 PM
CAS classification : [_separable]

\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

ode:=1+y(x)+(1-x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -1+\left (-1+x \right ) c_1 \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 18

ode=(1+y[x])+(1-x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.229 (sec). Leaf size: 8

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

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