Internal problem ID [4952]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (t^{2}+1\right ) y^{\prime }-t y+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve((t^2+1)*diff(y(t),t)=y(t)*t-y(t),y(t), singsol=all)
\[ y \left (t \right ) = c_{1} \sqrt {t^{2}+1}\, {\mathrm e}^{-\arctan \left (t \right )} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 28
DSolve[(t^2+1)*y'[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*}