12.7.5 problem 5

Internal problem ID [1715]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 5
Date solved : Saturday, March 29, 2025 at 11:36:26 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=2*y(x)^3+3*y(x)^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= c_1 \,{\mathrm e}^{-\frac {2 x}{3}} \\ \end{align*}

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 25

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

\begin{align*} y(x)\to 0 \\ y(x)\to c_1 e^{-2 x/3} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.174 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = C_{1} e^{- \frac {2 x}{3}} \]