12.7.4 problem 4

Internal problem ID [1714]
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 : 4
Date solved : Tuesday, March 04, 2025 at 01:37:55 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

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

\[ y = \frac {c_1}{x^{{3}/{2}}} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.113 (sec). Leaf size: 8

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

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