Internal problem ID [12690]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {2 t y}{t^{2}+1}=3} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(t),t)-2*t/(1+t^2)*y(t)=3,y(t), singsol=all)
\[ y \left (t \right ) = \left (t^{2}+1\right ) \left (3 \arctan \left (t \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 18
DSolve[y'[t]-2*t/(1+t^2)*y[t]==3,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \left (t^2+1\right ) (3 \arctan (t)+c_1) \]