8.5.23 problem 23

Internal problem ID [751]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 23
Date solved : Saturday, March 29, 2025 at 10:18:38 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 6 y+x y^{\prime }&=3 x y^{{4}/{3}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=6*y(x)+x*diff(y(x),x) = 3*x*y(x)^(4/3); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {1}{y^{{1}/{3}}}-x -c_1 \,x^{2} = 0 \]

✓ Mathematica. Time used: 0.149 (sec). Leaf size: 22

ode=6*y[x]+x*D[y[x],x] == 3*x*y[x]^(4/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{x^3 (1+c_1 x){}^3} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.333 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x*y(x)**(4/3) + x*Derivative(y(x), x) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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