74.6.5 problem 5

Internal problem ID [16028]
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
Date solved : Tuesday, January 28, 2025 at 08:28:03 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (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 &= 0 \\ y &= \sqrt {-3 t^{2}+c_{1}} \\ y &= -\sqrt {-3 t^{2}+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 49

DSolve[3*t*y[t]^2+y[t]^3*D[y[t],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*}