Internal problem ID [13039]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {t y}{t^{2}+1}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(diff(y(t),t)= t*y(t)/(1+t^2),y(t), singsol=all)
\[ y \left (t \right ) = c_{1} \sqrt {t^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 22
DSolve[y'[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*}