Internal problem ID [14239]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {2 t y}{t^{2}+1}=2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(t),t)-2*t/(1+t^2)*y(t)=2,y(t), singsol=all)
\[ y \left (t \right ) = \left (2 \arctan \left (t \right )+c_{1} \right ) \left (t^{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 18
DSolve[y'[t]-2*t/(1+t^2)*y[t]==2,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \left (t^2+1\right ) (2 \arctan (t)+c_1) \]