Internal
problem
ID
[9029]
Book
:
First
order
enumerated
odes
Section
:
section
1
Problem
number
:
45
Date
solved
:
Friday, February 21, 2025 at 09:03:41 PM
CAS
classification
:
[_quadrature]
Solve
Solving for the derivative gives these ODE’s to solve
Now each of the above is solved separately.
Solving Eq. (1)
Since the ode has the form \(y^{\prime }=f(x)\), then we only need to integrate \(f(x)\).
Solving Eq. (2)
Since the ode has the form \(y^{\prime }=f(x)\), then we only need to integrate \(f(x)\).
`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 <- differential order: 1; missing y(x) successful`
Solving time : 0.020
(sec)
Leaf size : 5
dsolve(x*sin(x)*diff(y(x),x)^2 = 0,y(x),singsol=all)
Solving time : 0.003
(sec)
Leaf size : 7
DSolve[{x*Sin[x]*D[y[x],x]^2==0,{}},y[x],x,IncludeSingularSolutions->True]
Solving time : 0.036
(sec)
Leaf size : 3
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*sin(x)*Derivative(y(x), x)**2,0) ics = {} dsolve(ode,func=y(x),ics=ics)
Eq(y(x), C1)