Internal
problem
ID
[8347]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
4.0
Problem
number
:
28
Date
solved
:
Sunday, November 10, 2024 at 03:39:00 AM
CAS
classification
:
[`y=_G(x,y')`]
Solve
Solving for the derivative gives these ODE’s to solve
Now each of the above is solved separately.
Solving Eq. (1)
Solving Eq. (2)
`Methods for first order ODEs: -> Solving 1st order ODE of high degree, 1st attempt trying 1st order WeierstrassP solution for high degree ODE trying 1st order WeierstrassPPrime solution for high degree ODE trying 1st order JacobiSN solution for high degree ODE trying 1st order ODE linearizable_by_differentiation trying differential order: 1; missing variables trying simple symmetries for implicit equations Successful isolation of dy/dx: 2 solutions were found. Trying to solve each resulting ODE. *** Sublevel 2 *** Methods for first order ODEs: --- Trying classification methods --- trying homogeneous types: trying exact Looking for potential symmetries trying an equivalence to an Abel ODE trying 1st order ODE linearizable_by_differentiation -> Solving 1st order ODE of high degree, Lie methods, 1st trial `, `-> Computing symmetries using: way = 3 `, `-> Computing symmetries using: way = 4 `, `-> Computing symmetries using: way = 2 `, `-> Computing symmetries using: way = 2 -> Solving 1st order ODE of high degree, 2nd attempt. Trying parametric methods trying dAlembert -> Calling odsolve with the ODE`, diff(y(x), x) = -x^2/(-2*(x^2+y(x)^2)^(5/4)*(((x^2+y(x)^2)^(1/2)-1)/(x^2+y(x)^2)^(1/2))^(1/2)+y(x) Methods for first order ODEs: --- Trying classification methods --- trying homogeneous types: trying exact Looking for potential symmetries trying an equivalence to an Abel ODE trying 1st order ODE linearizable_by_differentiation -> Calling odsolve with the ODE`, diff(y(x), x) = -x*(10+15*cos(2*y(x))+cos(6*y(x))+6*cos(4*y(x)))/(x*(16-6*x^2-2*x^2*(cos(4*y(x))+4 Methods for first order ODEs: --- Trying classification methods --- trying homogeneous types: trying exact Looking for potential symmetries trying an equivalence to an Abel ODE trying 1st order ODE linearizable_by_differentiation -> Solving 1st order ODE of high degree, Lie methods, 2nd trial `, `-> Computing symmetries using: way = 4 `, `-> Computing symmetries using: way = 5 `, `-> Computing symmetries using: way = 5`
Solving time : 0.139
(sec)
Leaf size : maple_leaf_size
dsolve(diff(y(x),x)^2+y(x)^2 = sec(x)^4, y(x),singsol=all)