29.11.4 problem 295

Internal problem ID [4895]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 295
Date solved : Sunday, March 30, 2025 at 04:09:26 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 9

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

\[ y = \tan \left (\arctan \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.292 (sec). Leaf size: 25

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

\begin{align*} y(x)\to \tan (\arctan (x)+c_1) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}

✓ Sympy. Time used: 0.280 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = \tan {\left (C_{1} + \operatorname {atan}{\left (x \right )} \right )} \]