14.1.3 problem 3

Internal problem ID [2474]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 3
Date solved : Sunday, March 30, 2025 at 12:02:31 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.246 (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)
 

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