13.2.3 problem 3

Internal problem ID [2301]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 3
Date solved : Saturday, March 29, 2025 at 11:53:17 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {t +c_1}{t^{2}+1} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 17

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

\[ y(t)\to \frac {t+c_1}{t^2+1} \]

✓ Sympy. Time used: 0.220 (sec). Leaf size: 10

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

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