72.8.11 problem 24

Internal problem ID [14775]
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. Review Exercises for chapter 1. page 136
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 07:14:59 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

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

\[ y = c_{1} \sqrt {t^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 22

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

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