Internal problem ID [14293]
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: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {3 t y^{2}+y^{3} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(3*t*y(t)^2+y(t)^3*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= 0 \\ y \left (t \right ) &= \sqrt {-3 t^{2}+c_{1}} \\ y \left (t \right ) &= -\sqrt {-3 t^{2}+c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 49
DSolve[3*t*y[t]^2+y[t]^3*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 0 \\ y(t)\to -\sqrt {-3 t^2+2 c_1} \\ y(t)\to \sqrt {-3 t^2+2 c_1} \\ y(t)\to 0 \\ \end{align*}