12.6.3 problem 3

Internal problem ID [1682]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 3
Date solved : Tuesday, March 04, 2025 at 01:31:06 PM
CAS classification : [_quadrature]

\begin{align*} 14 x^{2} y^{3}+21 x^{2} y^{2} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=14*x^2*y(x)^3+21*x^2*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: 0.025 (sec). Leaf size: 25

ode=(14*x^2*y[x]^3)+(21*x^2*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: 0.193 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(14*x**2*y(x)**3 + 21*x**2*y(x)**2*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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