1.5.42 problem 42

Internal problem ID [146]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 42
Date solved : Tuesday, September 30, 2025 at 03:47:13 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _exact, _rational]

\begin{align*} \frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \end{align*}

✓ Maple. Time used: 0.065 (sec). Leaf size: 185

ode:=1/2*(2*x^(5/2)-3*y(x)^(5/3))/x^(5/2)/y(x)^(2/3)+1/3*(3*y(x)^(5/3)-2*x^(5/2))/x^(3/2)/y(x)^(5/3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {2^{{3}/{5}} 3^{{2}/{5}} \left (x^{{5}/{2}}\right )^{{3}/{5}}}{3} \\ y &= -\frac {\left (i \sqrt {2}\, \sqrt {5-\sqrt {5}}+\sqrt {5}+1\right )^{3} 2^{{3}/{5}} 3^{{2}/{5}} \left (x^{{5}/{2}}\right )^{{3}/{5}}}{192} \\ y &= \frac {\left (i \sqrt {2}\, \sqrt {5-\sqrt {5}}-\sqrt {5}-1\right )^{3} 2^{{3}/{5}} 3^{{2}/{5}} \left (x^{{5}/{2}}\right )^{{3}/{5}}}{192} \\ y &= -\frac {\left (i \sqrt {2}\, \sqrt {5+\sqrt {5}}-\sqrt {5}+1\right )^{3} 2^{{3}/{5}} 3^{{2}/{5}} \left (x^{{5}/{2}}\right )^{{3}/{5}}}{192} \\ y &= \frac {\left (i \sqrt {2}\, \sqrt {5+\sqrt {5}}+\sqrt {5}-1\right )^{3} 2^{{3}/{5}} 3^{{2}/{5}} \left (x^{{5}/{2}}\right )^{{3}/{5}}}{192} \\ \frac {x}{y^{{2}/{3}}}+\frac {y}{x^{{3}/{2}}}+c_1 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 260

ode=( (2*x^(5/2)-3*y[x]^(5/3))/( 2*x^(5/2)*y[x]^(2/3)) )+(   (3*y[x]^(5/3)-2*x^(5/2))/( 3*x^(3/2)*y[x]^(5/3) ) )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \left (\frac {2}{3}\right )^{3/5} \left (x^{5/2}\right )^{3/5}\\ y(x)&\to c_1 x^{3/2}\\ y(x)&\to -\left (-\frac {2}{3}\right )^{3/5} x^{3/2}\\ y(x)&\to \left (-\frac {2}{3}\right )^{3/5} x^{3/2}\\ y(x)&\to -\left (\frac {2}{3}\right )^{3/5} x^{3/2}\\ y(x)&\to \left (\frac {2}{3}\right )^{3/5} x^{3/2}\\ y(x)&\to -\sqrt [5]{-1} \left (\frac {2}{3}\right )^{3/5} x^{3/2}\\ y(x)&\to \sqrt [5]{-1} \left (\frac {2}{3}\right )^{3/5} x^{3/2}\\ y(x)&\to -(-1)^{2/5} \left (\frac {2}{3}\right )^{3/5} x^{3/2}\\ y(x)&\to (-1)^{2/5} \left (\frac {2}{3}\right )^{3/5} x^{3/2}\\ y(x)&\to -(-1)^{4/5} \left (\frac {2}{3}\right )^{3/5} x^{3/2}\\ y(x)&\to (-1)^{4/5} \left (\frac {2}{3}\right )^{3/5} x^{3/2}\\ y(x)&\to \left (\frac {2}{3}\right )^{3/5} \left (x^{5/2}\right )^{3/5} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-2*x**(5/2) + 3*y(x)**(5/3))*Derivative(y(x), x)/(3*x**(3/2)*y(x)**(5/3)) + (2*x**(5/2) - 3*y(x)**(5/3))/(2*x**(5/2)*y(x)**(2/3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : NoneType object is not subscriptable