58.4.1 problem 1

Internal problem ID [14571]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:42:25 AM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+4 y x&=0 \end{align*}

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

ode:=4*x*y(x)+(x^2+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1}{\left (x^{2}+1\right )^{2}} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 20

ode=(4*x*y[x])+(x^2+1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.146 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*y(x) + (x**2 + 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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