85.15.12 problem 2 (b)

Internal problem ID [22537]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 47
Problem number : 2 (b)
Date solved : Thursday, October 02, 2025 at 08:48:38 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=-3 \\ \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 13

ode:=2*x*y(x)+(x^2+1)*diff(y(x),x) = 0; 
ic:=[y(1) = -3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {6}{x^{2}+1} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 14

ode=2*x*y[x]+(x^2+1)*D[y[x],x]==0; 
ic={y[1]==-3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {6}{x^2+1} \end{align*}

✓ Sympy. Time used: 0.132 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x) + (x**2 + 1)*Derivative(y(x), x),0) 
ics = {y(1): -3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {6}{x^{2} + 1} \]