87.4.12 problem 12

Internal problem ID [23278]
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 37
Problem number : 12
Date solved : Thursday, October 02, 2025 at 09:28:15 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-\frac {x}{x^{2}+1}&=-\frac {x y}{x^{2}+1} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(x),x)-x/(x^2+1) = -x/(x^2+1)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = 1+\frac {c_1}{\sqrt {x^{2}+1}} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 24

ode=D[y[x],x]-x/(1+x^2)== -x/(1+x^2)*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 1+\frac {c_1}{\sqrt {x^2+1}}\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.215 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x)/(x**2 + 1) - x/(x**2 + 1) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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