17.6.8 problem 1.2-1 (h)

Internal problem ID [3445]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-1, page 12
Problem number : 1.2-1 (h)
Date solved : Monday, January 27, 2025 at 07:36:56 AM
CAS classification : [_linear]

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

✓ 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)
 

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 26

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

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