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 : Monday, January 27, 2025 at 05:45:00 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: 0.001 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

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

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

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