Internal problem ID [12554]
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. Exercises section 1.2. page
33
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {t}{t^{2} y+y}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(t),t)=t/(t^2*y(t)+y(t)),y(t), singsol=all)
\begin{align*} y \left (t \right ) = \sqrt {\ln \left (t^{2}+1\right )+c_{1}} y \left (t \right ) = -\sqrt {\ln \left (t^{2}+1\right )+c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.162 (sec). Leaf size: 41
DSolve[y'[t]==t/(t^2*y[t]+y[t]),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sqrt {\log \left (t^2+1\right )+2 c_1} y(t)\to \sqrt {\log \left (t^2+1\right )+2 c_1} \end{align*}