8.6.26 problem 26

Internal problem ID [796]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 26
Date solved : Saturday, March 29, 2025 at 10:28:44 PM
CAS classification : [[_homogeneous, `class G`], _exact, _rational]

\begin{align*} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 43

ode:=9*x^(1/2)*y(x)^(4/3)-12*x^(1/5)*y(x)^(3/2)+(8*x^(3/2)*y(x)^(1/3)-15*x^(6/5)*y(x)^(1/2))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ -125 y^{{9}/{2}} x^{{18}/{5}}+225 y^{{13}/{3}} x^{{39}/{10}}-135 y^{{25}/{6}} x^{{21}/{5}}+27 y^{4} x^{{9}/{2}}-c_1 = 0 \]

✗ Mathematica

ode=9*x^(1/2)*y[x]^(4/3)-12*x^(1/5)*y[x]^(3/2)+(8*x^(3/2)*y[x]^(1/3)-15*x^(6/5)*y[x]^(1/2))*D[y[x],x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*x**(1/5)*y(x)**(3/2) + 9*sqrt(x)*y(x)**(4/3) + (-15*x**(6/5)*sqrt(y(x)) + 8*x**(3/2)*y(x)**(1/3))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out