Internal problem ID [1651]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\frac {2 t y}{t^{2}+1}+y^{\prime }-\frac {1}{t^{2}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve(2*t*y(t)/(t^2+1)+diff(y(t),t) = 1/(t^2+1),y(t), singsol=all)
\[ y \relax (t ) = \frac {t +c_{1}}{t^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 17
DSolve[2*t*y[t]/(t^2+1)+y'[t] == 1/(t^2+1),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {t+c_1}{t^2+1} \\ \end{align*}