74.7.16 problem 16

Internal problem ID [16093]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 08:39:36 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 45

dsolve(( sqrt(t^2+1)  )+( y(t) )*diff(y(t),t)=0,y(t), singsol=all)
 

\begin{align*} y &= \sqrt {-t \sqrt {t^{2}+1}-\operatorname {arcsinh}\left (t \right )+c_{1}} \\ y &= -\sqrt {-t \sqrt {t^{2}+1}-\operatorname {arcsinh}\left (t \right )+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.799 (sec). Leaf size: 61

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

\begin{align*} y(t)\to -\sqrt {-\text {arcsinh}(t)-\sqrt {t^2+1} t+2 c_1} \\ y(t)\to \sqrt {-\text {arcsinh}(t)-\sqrt {t^2+1} t+2 c_1} \\ \end{align*}