76.5.18 problem 18

Internal problem ID [17438]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 10:36:24 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 3 y^{\prime } t +9 y&=2 t y^{{5}/{3}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(3*t*diff(y(t),t)+9*y(t)=2*t*y(t)^(5/3),y(t), singsol=all)
 

\[ \frac {1}{y^{{2}/{3}}}-\frac {4 t}{9}-c_{1} t^{2} = 0 \]

✓ Solution by Mathematica

Time used: 0.468 (sec). Leaf size: 25

DSolve[3*t*D[y[t],t]+9*y[t]==2*t*y[t]^(5/3),y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {27}{(t (4+9 c_1 t)){}^{3/2}} \\ y(t)\to 0 \\ \end{align*}