12.7.21 problem 22

Internal problem ID [1731]
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 : 22
Date solved : Tuesday, March 04, 2025 at 01:40:55 PM
CAS classification : [_separable]

\begin{align*} x^{4} y^{4}+x^{5} y^{3} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=x^4*y(x)^4+x^5*y(x)^3*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= \frac {c_1}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 21

ode=(x^4*y[x]^4)+(x^5*y[x]^3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to 0 \\ y(x)\to \frac {c_1}{x} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.167 (sec). Leaf size: 5

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**5*y(x)**3*Derivative(y(x), x) + x**4*y(x)**4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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