Internal problem ID [14359]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } y=-\sqrt {t^{2}+1}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
dsolve(( sqrt(t^2+1) )+( y(t) )*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \sqrt {-t \sqrt {t^{2}+1}-\operatorname {arcsinh}\left (t \right )+c_{1}} \\ y \left (t \right ) &= -\sqrt {-t \sqrt {t^{2}+1}-\operatorname {arcsinh}\left (t \right )+c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.194 (sec). Leaf size: 81
DSolve[( Sqrt[t^2+1] )+( y[t] )*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sqrt {-\sqrt {t^2+1} t+\log \left (\sqrt {t^2+1}-t\right )+2 c_1} \\ y(t)\to \sqrt {-\sqrt {t^2+1} t+\log \left (\sqrt {t^2+1}-t\right )+2 c_1} \\ \end{align*}