74.6.19 problem 20

Internal problem ID [16042]
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 : 20
Date solved : Tuesday, January 28, 2025 at 08:28:51 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

\begin{align*} 3 t^{2}+3 y^{2}+6 t y y^{\prime }&=0 \end{align*}

Solution by Maple

Time used: 0.007 (sec). Leaf size: 47

dsolve((3*t^2+3*y(t)^2)+6*t*y(t)*diff(y(t),t)=0,y(t), singsol=all)
 
\begin{align*} y &= -\frac {\sqrt {3}\, \sqrt {-t \left (t^{3}-3 c_{1} \right )}}{3 t} \\ y &= \frac {\sqrt {3}\, \sqrt {-t \left (t^{3}-3 c_{1} \right )}}{3 t} \\ \end{align*}

Solution by Mathematica

Time used: 0.220 (sec). Leaf size: 60

DSolve[(3*t^2+3*y[t]^2)+6*t*y[t]*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 
\begin{align*} y(t)\to -\frac {\sqrt {-t^3+3 c_1}}{\sqrt {3} \sqrt {t}} \\ y(t)\to \frac {\sqrt {-t^3+3 c_1}}{\sqrt {3} \sqrt {t}} \\ \end{align*}