Differential Equations

From apimba
Revision as of 18:06, 5 May 2020 by Milllo (talk | contribs)
Jump to navigation Jump to search

The integral character ∫

Method for solving linear differential equations:

  1. Put equation into standard form: dy/dx + f(x)y = g(x)
  2. Find the integrating factor: u(x) which is equal to e∫f(x)dx, so du/dx = u(x)f(x)
  3. multiply the standard form by u(x): u(x)dy/dx + u(x)f(x)y = u(x)g(x)
  4. use the product rule (udy/dx + ydu/dx = (u,y)d/dx) on the left side: d/dx(u(x),y(x)) = u(x)g(x)
  5. integrate both sides, use sources such as table of integrals: u(x)y(x) = ∫u(x)g(x)dx
  6. solve for y

Examples