74.7.21 problem 21

Internal problem ID [16098]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 08:40:28 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 56

dsolve(( t^3+y(t)^3 )-( t*y(t)^2 )*diff(y(t),t)=0,y(t), singsol=all)
 

\begin{align*} y &= \left (3 \ln \left (t \right )+c_{1} \right )^{{1}/{3}} t \\ y &= -\frac {\left (3 \ln \left (t \right )+c_{1} \right )^{{1}/{3}} \left (1+i \sqrt {3}\right ) t}{2} \\ y &= \frac {\left (3 \ln \left (t \right )+c_{1} \right )^{{1}/{3}} \left (i \sqrt {3}-1\right ) t}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.180 (sec). Leaf size: 63

DSolve[( t^3+y[t]^3 )-( t*y[t]^2 )*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to t \sqrt [3]{3 \log (t)+c_1} \\ y(t)\to -\sqrt [3]{-1} t \sqrt [3]{3 \log (t)+c_1} \\ y(t)\to (-1)^{2/3} t \sqrt [3]{3 \log (t)+c_1} \\ \end{align*}