29.13.3 problem 357

Internal problem ID [4957]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 357
Date solved : Tuesday, March 04, 2025 at 07:34:49 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.248 (sec). Leaf size: 10

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

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