88.12.18 problem 20

Internal problem ID [24074]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 20
Date solved : Thursday, October 02, 2025 at 09:57:04 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.214 (sec). Leaf size: 35

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

\[ -\frac {\ln \left (\frac {x^{2}+y^{2}}{x^{2}}\right )}{2}-2 \ln \left (\frac {y}{x}\right )-\ln \left (x \right )-c_1 = 0 \]

✓ Mathematica. Time used: 60.13 (sec). Leaf size: 1198

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out