83.45.19 problem Ex 19 page 60

Internal problem ID [19491]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter IV. Equations of the first order but not of the first degree
Problem number : Ex 19 page 60
Date solved : Monday, March 31, 2025 at 07:24:04 PM
CAS classification : [_rational]

\begin{align*} 3 {y^{\prime }}^{2} y-2 x y y^{\prime }+4 y^{2}-x^{2}&=0 \end{align*}

✗ Maple

ode:=3*y(x)*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)+4*y(x)^2-x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=3*D[y[x],x]^2*y[x]-2*x*y[x]*D[y[x],x]+4*y[x]^2-x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

Timed Out