13.2.8 problem 8

Internal problem ID [2306]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 8
Date solved : Monday, January 27, 2025 at 05:45:09 AM
CAS classification : [_separable]

\begin{align*} \sqrt {t^{2}+1}\, y+y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=\sqrt {5} \end{align*}

✓ Solution by Maple

Time used: 0.023 (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)
 

\[ y = \sqrt {5}\, {\mathrm e}^{-\frac {t \sqrt {t^{2}+1}}{2}-\frac {\operatorname {arcsinh}\left (t \right )}{2}} \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 34

DSolve[{(t^2+1)^(1/2)*y[t]+D[y[t],t] == 0,y[0]==Sqrt[5]},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \sqrt {5} e^{-\frac {\text {arcsinh}(t)}{2}-\frac {1}{2} \sqrt {t^2+1} t} \]