Internal problem ID [1656]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\sqrt {t^{2}+1}\, y+y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = \sqrt {5}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 24
dsolve([(t^2+1)^(1/2)*y(t)+diff(y(t),t) = 0,y(0) = 5^(1/2)],y(t), singsol=all)
\[ y \relax (t ) = \sqrt {5}\, {\mathrm e}^{-\frac {t \sqrt {t^{2}+1}}{2}-\frac {\arcsinh \relax (t )}{2}} \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 44
DSolve[{(t^2+1)^(1/2)*y[t]+y'[t] == 0,y[0]==Sqrt[5]},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \sqrt {5} e^{-\frac {1}{2} t \sqrt {t^2+1}} \sqrt {\sqrt {t^2+1}-t} \\ \end{align*}