60.1.326 problem 333

Internal problem ID [10340]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 333
Date solved : Wednesday, March 05, 2025 at 10:21:20 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 38

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

\[ -\frac {3 \left (\frac {\left (c_{1} +\frac {3 \ln \left (x \right )}{2}-3 \ln \left (y\right )\right ) x^{{3}/{2}} y^{{3}/{2}}}{3}+x y-\frac {1}{3}\right )}{y^{{3}/{2}} x^{{3}/{2}}} = 0 \]

✓ Mathematica. Time used: 0.298 (sec). Leaf size: 72

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

\[ \text {Solve}\left [\frac {2 \sqrt {x y(x)} \log (y(x))}{\sqrt {x} \sqrt {y(x)}}-\frac {\sqrt {x y(x)} \left (3 x^{3/2} y(x)^{3/2} \log (x)+6 x y(x)-2\right )}{3 x^2 y(x)^2}=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out