80.7.1 problem 1 (eq 98)

Internal problem ID [18500]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter V. Singular solutions. section 36. Problems at page 99
Problem number : 1 (eq 98)
Date solved : Thursday, March 13, 2025 at 12:08:49 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} 4 y {y^{\prime }}^{3}-2 x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }+x^{3}&=16 y^{2} \end{align*}

✗ Maple

ode:=4*y(x)*diff(y(x),x)^3-2*x^2*diff(y(x),x)^2+4*x*y(x)*diff(y(x),x)+x^3 = 16*y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 50.04 (sec). Leaf size: 49162

ode=4*y[x]*D[y[x],x]^3-2*x^2*D[y[x],x]^2+4*x*y[x]*D[y[x],x]+x^3==16*y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3 - 2*x**2*Derivative(y(x), x)**2 + 4*x*y(x)*Derivative(y(x), x) - 16*y(x)**2 + 4*y(x)*Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out