Connection: Differential Equations vs. Algebraic Equations

  1. Exercise: solve the differential equation y' = cos x.
  2. Exercise: solve the algebraic equation x^2+5x+6=0.
  3. Can you identify an important difference between the solutions of these two types of equations?

Answer:

  1. y=sin x + C where C is an arbitrary constant. Note that the solution y is a function of x.
  2. x=-2,-3.
  3. Solutions to differential equations are functions, whereas solutions to algebraic equations are numbers.

Note: I am currently working on displaying equations properly. For now, x^2 denotes x to the second power ("x squared").

Icon for Higher Math Notes: Differential Equations (A Higher Math Help Resource)

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