8.6.22 problem 22

Internal problem ID [792]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 22
Date solved : Tuesday, March 04, 2025 at 11:48:48 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }&=12 x^{4} y^{{2}/{3}}+6 y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=x*diff(y(x),x) = 12*x^4*y(x)^(2/3)+6*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ -2 x^{4}-c_1 \,x^{2}+y^{{1}/{3}} = 0 \]

✓ Mathematica. Time used: 0.155 (sec). Leaf size: 19

ode=x*D[y[x],x]== 12*x^4*y[x]^(2/3)+6*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^6 \left (2 x^2+c_1\right ){}^3 \]

✓ Sympy. Time used: 0.260 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*x**4*y(x)**(2/3) + x*Derivative(y(x), x) - 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{6} \left (C_{1}^{3} + 6 C_{1}^{2} x^{2} + 12 C_{1} x^{4} + 8 x^{6}\right ) \]