20.2.5 problem Problem 5

Internal problem ID [3597]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential Equations. page 43
Problem number : Problem 5
Date solved : Sunday, March 30, 2025 at 01:53:52 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 16

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

\begin{align*} y(x)\to c_1 (x-1) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.202 (sec). Leaf size: 7

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

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