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 : Monday, January 27, 2025 at 05:53:39 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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