6.5 problem 5

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*}