Difference between revisions of "Differential Equations"

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# Find the integrating factor: u(x) which is equal to e<sup>∫f(x)dx</sup>, so du/dx = f(x)u(x)
 
# Find the integrating factor: u(x) which is equal to e<sup>∫f(x)dx</sup>, so du/dx = f(x)u(x)
 
# multiply the standard form by u(x): u(x)dy/dx + u(x)f(x)y = u(x)g(x)
 
# multiply the standard form by u(x): u(x)dy/dx + u(x)f(x)y = u(x)g(x)
# 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)
+
# 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)
 
# integrate both sides
 
# integrate both sides
 
# solve for y
 
# solve for y

Revision as of 05:33, 5 May 2020

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 = f(x)u(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
  6. solve for y