Internal
problem
ID
[9131]
Book
:
Second
order
enumerated
odes
Section
:
section
2
Problem
number
:
9
Date
solved
:
Sunday, February 23, 2025 at 05:33:27 AM
CAS
classification
:
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve
`Methods for second order ODEs: --- Trying classification methods --- trying 2nd order Liouville <- 2nd_order Liouville successful`
Solving time : 0.011
(sec)
Leaf size : 32
dsolve(diff(diff(y(x),x),x)+(x+3)*diff(y(x),x)+(y(x)^2+3)*diff(y(x),x)^2 = 0,y(x),singsol=all)
Solving time : 9.111
(sec)
Leaf size : 56
DSolve[{D[y[x],{x,2}]+(3+x)*D[y[x],x]+(3+y[x]^2)*(D[y[x],x])^2==0,{}},y[x],x,IncludeSingularSolutions->True]
Solving time : 0.000
(sec)
Leaf size : 0
Python version: 3.13.1 (main, Dec 4 2024, 18:05:56) [GCC 14.2.1 20240910] Sympy version 1.13.3
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