15.8.51 problem 54

Internal problem ID [3054]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 54
Date solved : Sunday, March 30, 2025 at 01:14:35 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

With initial conditions

\begin{align*} y \left (2\right )&=1 \end{align*}

✓ Maple. Time used: 44.507 (sec). Leaf size: 256

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

\[ y = \frac {\sqrt {10}\, x^{2}}{\left (x^{6} {\left (\sqrt {\frac {\left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{2}/{3}}+20}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{1}/{3}}}}+\sqrt {\frac {4 \sqrt {10}\, x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{1}/{3}}-\sqrt {\frac {\left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{2}/{3}}+20}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{1}/{3}}}}\, \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{2}/{3}}-20 \sqrt {\frac {\left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{2}/{3}}+20}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{1}/{3}}}}}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{1}/{3}} \sqrt {\frac {\left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{2}/{3}}+20}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{1}/{3}}}}}}\right )}^{3}\right )^{{1}/{3}}} \]

✗ Mathematica

ode=y[x]^2+(x^3-2*x*y[x])*D[y[x],x]==0; 
ic={y[2]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x**3 - 2*x*y(x))*Derivative(y(x), x) + y(x)**2,0) 
ics = {y(2): 1} 
dsolve(ode,func=y(x),ics=ics)