7.7.22 problem 22

Internal problem ID [200]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 22
Date solved : Tuesday, March 04, 2025 at 11:01:30 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.166 (sec). Leaf size: 19

ode=x*D[y[x],x]==6*y[x]+12*x^4*y[x]^(2/3); 
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: 0.289 (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)
 

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