First order linear DEs, separable DEs

Learning objectives

  • Work with models using 1st order linear equations
  • Solve equations that can be put in the form a(y)dy = b(t)dt
  • Recognize 1st order linear DEs:  dy/dt + p(t)y = f(t)
    • undriven (aka homogeneous) if f(t) = 0, otherwise driven
  • Solve 1st order linear DEs
    • y(t) = Cy_u(t) + y_d(t) where
    • y_u and y_d are ANY single solutions (y_u \ne 0) of the undriven (y^\prime + py = 0) and driven (y^\prime + py = f) DEs
  • Find y_u and y_d
  • Uniqueness and existence theorems for 1st order linear DEs

In class

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