32.5.6 problem Exercise 11.6, page 97

Internal problem ID [5844]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.6, page 97
Date solved : Tuesday, March 04, 2025 at 11:48:01 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 16

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

\[ y(x)\to \left (x^2+1\right ) (\arctan (x)+c_1) \]

✓ Sympy. Time used: 0.399 (sec). Leaf size: 49

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

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