Internal problem ID [1657]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 22
dsolve((t^2+1)^(1/2)*y(t)/exp(t)+diff(y(t),t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} {\mathrm e}^{\int -\sqrt {t^{2}+1}\, {\mathrm e}^{-t}d t} \]
✓ Solution by Mathematica
Time used: 0.279 (sec). Leaf size: 40
DSolve[(t^2+1)^(1/2)*y[t]/Exp[t]+y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 \exp \left (\int _1^t-e^{-K[1]} \sqrt {K[1]^2+1}dK[1]\right ) \\ y(t)\to 0 \\ \end{align*}