87.3.4 problem 4

Internal problem ID [23253]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 26
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:27:07 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }+y&=3 \end{align*}

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

ode:=x*diff(y(x),x)+y(x) = 3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3 x +c_1}{x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 18

ode=x*D[y[x],x]+y[x]==3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3+\frac {c_1}{x}\\ y(x)&\to 3 \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + y(x) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x} + 3 \]