Internal
problem
ID
[8157]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
1.0
Problem
number
:
19
Date
solved
:
Sunday, November 10, 2024 at 03:05:50 AM
CAS
classification
:
[`y=_G(x,y')`]
Solve
Unknown ode type.
`Methods for first order ODEs: --- Trying classification methods --- trying homogeneous types: differential order: 1; looking for linear symmetries trying exact Looking for potential symmetries trying an equivalence to an Abel ODE trying 1st order ODE linearizable_by_differentiation --- Trying Lie symmetry methods, 1st order --- `, `-> Computing symmetries using: way = 3 `, `-> Computing symmetries using: way = 5 trying symmetry patterns for 1st order ODEs -> trying a symmetry pattern of the form [F(x)*G(y), 0] -> trying a symmetry pattern of the form [0, F(x)*G(y)] -> trying symmetry patterns of the forms [F(x),G(y)] and [G(y),F(x)] -> trying a symmetry pattern of the form [F(x),G(x)] -> trying a symmetry pattern of the form [F(y),G(y)] -> trying a symmetry pattern of the form [F(x)+G(y), 0] -> trying a symmetry pattern of the form [0, F(x)+G(y)] -> trying a symmetry pattern of the form [F(x),G(x)*y+H(x)] -> trying a symmetry pattern of conformal type`
Solving time : 0.019
(sec)
Leaf size : maple_leaf_size
dsolve(diff(y(x),x) = (1-x^2-y(x)^2)^(1/2), y(x),singsol=all)