36.2.3 problem 3

Internal problem ID [6296]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 3
Date solved : Monday, January 27, 2025 at 01:55:15 PM
CAS classification : [_separable]

\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=y t -y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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

\[ y = c_{1} \sqrt {t^{2}+1}\, {\mathrm e}^{-\arctan \left (t \right )} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 28

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

\begin{align*} y(t)\to c_1 \sqrt {t^2+1} e^{-\arctan (t)} \\ y(t)\to 0 \\ \end{align*}