84.11.1 problem 6.1

Internal problem ID [22138]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 6. Exact first-order differential equations. Solved problems. Page 24
Problem number : 6.1
Date solved : Thursday, October 02, 2025 at 08:31:36 PM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \end{align*}

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

ode:=2*x*y(x)+(x^2+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 20

ode=(2*x*y[x])+(1+x^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{x^2+1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.128 (sec). Leaf size: 8

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

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