83.3.4 problem 4

Internal problem ID [18981]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (B) at page 9
Problem number : 4
Date solved : Thursday, March 13, 2025 at 01:16:30 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 10

ode:=2*y(x)+(x^2+1)*arctan(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.135 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.291 (sec). Leaf size: 8

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

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