Internal
problem
ID
[9131]
Book
:
Second
order
enumerated
odes
Section
:
section
2
Problem
number
:
9
Date
solved
:
Thursday, March 13, 2025 at 06:58:34 PM
CAS
classification
:
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve
ode:=diff(diff(y(x),x),x)+(x+3)*diff(y(x),x)+(3+y(x)^2)*diff(y(x),x)^2 = 0; dsolve(ode,y(x), singsol=all);
Maple trace
`Methods for second order ODEs: --- Trying classification methods --- trying 2nd order Liouville <- 2nd_order Liouville successful`
ode=D[y[x],{x,2}]+(3+x)*D[y[x],x]+(3+y[x]^2)*(D[y[x],x])^2==0; ic={}; DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
from sympy import * x = symbols("x") y = Function("y") ode = Eq((x + 3)*Derivative(y(x), x) + (y(x)**2 + 3)*Derivative(y(x), x)**2 + Derivative(y(x), (x, 2)),0) ics = {} dsolve(ode,func=y(x),ics=ics)
NotImplementedError : The given ODE Derivative(y(x), x) - (-x + sqrt(x**2 + 6*x - 4*y(x)**2*Derivative(y(x), (x, 2)) - 12*Derivative(y(x), (x, 2)) + 9) - 3)/(2*(y(x)**2 + 3)) cannot be solved by the factorable group method