74.6.12 problem 13

Internal problem ID [16035]
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 : 13
Date solved : Tuesday, January 28, 2025 at 08:28:29 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 32

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

\begin{align*} y &= 0 \\ y &= \frac {\sqrt {-c_{1} t}}{t} \\ y &= -\frac {\sqrt {-c_{1} t}}{t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 23

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

\begin{align*} y(t)\to 0 \\ y(t)\to \frac {c_1}{\sqrt {t}} \\ y(t)\to 0 \\ \end{align*}