Internal problem ID [1965]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.2-1, page 12
Problem number: 1.2-1 (h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 t y}{t^{2}+1}-t -1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 22
dsolve(diff(y(t),t)=2*t/(t^2+1)*y(t)+t+1,y(t), singsol=all)
\[ y \relax (t ) = \left (\frac {\ln \left (t^{2}+1\right )}{2}+\arctan \relax (t )+c_{1}\right ) \left (t^{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 26
DSolve[y'[t]==2*t/(t^2+1)*y[t]+t+1,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \left (t^2+1\right ) \left (\text {ArcTan}(t)+\frac {1}{2} \log \left (t^2+1\right )+c_1\right ) \\ \end{align*}