15.8.53 problem 56

Internal problem ID [3056]
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 : 56
Date solved : Sunday, March 30, 2025 at 01:14:42 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

With initial conditions

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

✓ Maple. Time used: 1.429 (sec). Leaf size: 73

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

\[ y = \frac {\sqrt {3}\, \sqrt {2}\, \sqrt {\frac {\left (54 x^{4}+6 \sqrt {3}\, \sqrt {27 x^{8}-2 x^{6}}\right )^{{2}/{3}}+6 x^{2}}{\left (54 x^{4}+6 \sqrt {3}\, \sqrt {27 x^{8}-2 x^{6}}\right )^{{1}/{3}}}}}{6} \]

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out