7.4.5 problem 7

Internal problem ID [2342]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.9. Page 66
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 11:12:25 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.072 (sec). Leaf size: 7

ode:=2*t*y(t)^3+3*t^2*y(t)^2*diff(y(t),t) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {1}{t^{{2}/{3}}} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 10

ode=2*t*y[t]^3+3*t^2*y[t]^2*D[y[t],t] == 0; 
ic=y[1]==1; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{t^{2/3}} \end{align*}

✓ Sympy. Time used: 0.115 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*t**2*y(t)**2*Derivative(y(t), t) + 2*t*y(t)**3,0) 
ics = {y(1): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {1}{t^{\frac {2}{3}}} \]