Internal problem ID [14290]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\frac {t}{\sqrt {y^{2}+t^{2}}}+\frac {y y^{\prime }}{\sqrt {y^{2}+t^{2}}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(t/sqrt(t^2+y(t)^2)+y(t)/sqrt(t^2+y(t)^2)*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \sqrt {-t^{2}+c_{1}} \\ y \left (t \right ) &= -\sqrt {-t^{2}+c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 39
DSolve[t/Sqrt[t^2+y[t]^2]+y[t]/Sqrt[t^2+y[t]^2]*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sqrt {-t^2+2 c_1} \\ y(t)\to \sqrt {-t^2+2 c_1} \\ \end{align*}