14.3.5 problem 7

Internal problem ID [2514]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.9. Exact equations. Excercises page 66
Problem number : 7
Date solved : Sunday, March 30, 2025 at 12:06:21 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,ic],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.031 (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]
 

\[ y(t)\to \frac {1}{t^{2/3}} \]

✓ Sympy. Time used: 0.182 (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)
 

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