How to solve an ODE in the form y' = c + k*sin(y)

  • Thread starter Thread starter AsifHirai
  • Start date Start date
  • Tags Tags
    Form Ode
Click For Summary
SUMMARY

The discussion focuses on solving the ordinary differential equation (ODE) in the form y' = c + k*sin(y). The user seeks assistance in finding a solution, particularly when c and k are independent of y, making the equation separable. The integral line for the solution is expressed as x + Constant = ∫ (dy / (c + k*sin(y))). This integral can be graphed to visualize the solution when an exact solution is not available.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with integral calculus
  • Knowledge of separable differential equations
  • Basic graphing techniques for visualizing integrals
NEXT STEPS
  • Study methods for solving separable differential equations
  • Learn about integral calculus techniques for evaluating complex integrals
  • Explore numerical methods for approximating solutions to ODEs
  • Investigate graphing tools or software for visualizing integral solutions
USEFUL FOR

Mathematicians, engineering students, and anyone involved in solving differential equations or performing torque calculations will benefit from this discussion.

AsifHirai
Messages
4
Reaction score
0
I managed to stumble upon a differential equation such as the one above while doing some torque calculations and am wondering if and how to find the solution to it.
I'm not that well versed in differential equations, so any help would be appreciated.

Edit:
A method to graph an integral line for the solution would be appreciated if there is no exact solution
 
Last edited:
Physics news on Phys.org
If c and k are independent of y it is separable

$$x+\mathrm{Constant}=\int \frac{\mathrm{d}y}{c+k \, \sin(y)}$$
 

Similar threads

Undergrad ODE with non-exact solution: closed-form, non-iterative approximations
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Seeking advice about solving an ODE
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Solving an ODE with Legendre Polynomials
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Can the ODE \psi''-y^2\psi=0 be solved using a general method?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Searching for radial part solution of Klein-Gordon type equation
  • · Replies 1 ·
Replies
1
Views
2K
MHB Help with a question (Bernoulli General solution)
  • · Replies 8 ·
Replies
8
Views
2K
MHB Solving a Non-Exact ODE: $(y-2x^2y)dx +xdy = 0$
  • · Replies 4 ·
Replies
4
Views
2K
Mathematica - How to Graph Direction Fields of ODEs?
  • · Replies 9 ·
Replies
9
Views
2K
Linear homogenous ODEs with constant coefficients
  • · Replies 2 ·
Replies
2
Views
2K
Solving ODE: Get Help with y''(x)+(μ^2*c(x)+k^2)y=0
  • · Replies 4 ·
Replies
4
Views
2K