89.1.10 problem 10

Internal problem ID [24245]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 21
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:01:31 PM
CAS classification : [_separable]

\begin{align*} y x -\left (x +2\right ) y^{\prime }&=0 \end{align*}

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

ode:=x*y(x)-(x+2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,{\mathrm e}^{x}}{\left (x +2\right )^{2}} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 21

ode=(x*y[x])-(x+2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1 e^x}{(x+2)^2}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.158 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \frac {C_{1} e^{x}}{x^{2} + 4 x + 4} \]