76.5.18 problem 18

Internal problem ID [17367]
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 : Monday, March 31, 2025 at 04:08:38 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ \frac {1}{y^{{2}/{3}}}-\frac {4 t}{9}-t^{2} c_1 = 0 \]

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

ode=3*t*D[y[t],t]+9*y[t]==2*t*y[t]^(5/3); 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 2.369 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*t*y(t)**(5/3) + 3*t*Derivative(y(t), t) + 9*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = - 27 \left (\frac {1}{t \left (C_{1} t + 4\right )}\right )^{\frac {3}{2}}, \ y{\left (t \right )} = 27 \left (\frac {1}{t \left (C_{1} t + 4\right )}\right )^{\frac {3}{2}}\right ] \]