74.6.2 problem 2

Internal problem ID [16025]
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
Date solved : Tuesday, January 28, 2025 at 08:27:45 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (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 &= \sqrt {-t^{2}+c_{1}} \\ y &= -\sqrt {-t^{2}+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.083 (sec). Leaf size: 39

DSolve[t/Sqrt[t^2+y[t]^2]+y[t]/Sqrt[t^2+y[t]^2]*D[y[t],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*}