Internal problem ID [14308]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]
\[ \boxed {3 y^{2}+6 t y y^{\prime }=-3 t^{2}} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (t \right ) &= -\frac {\sqrt {3}\, \sqrt {-t \left (t^{3}-3 c_{1} \right )}}{3 t} \\ y \left (t \right ) &= \frac {\sqrt {3}\, \sqrt {-t \left (t^{3}-3 c_{1} \right )}}{3 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.196 (sec). Leaf size: 60
DSolve[(3*t^2+3*y[t]^2)+6*t*y[t]*y'[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*}