19.1.9 problem 9

Internal problem ID [4221]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 9
Date solved : Tuesday, September 30, 2025 at 07:07:38 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {4 x y}{x^{2}+1} \end{align*}

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

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

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

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

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

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

✓ Sympy. Time used: 0.133 (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)
 

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