74.5.10 problem 10

Internal problem ID [15974]
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
Date solved : Tuesday, January 28, 2025 at 08:25:14 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve(diff(y(t),t)-2*t/(1+t^2)*y(t)=2,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 31

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

\[ y(t)\to \left (t^2+1\right ) \left (\int _1^t\frac {2}{K[1]^2+1}dK[1]+c_1\right ) \]