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How to Calculate a Constant

The derivative of a constant is zero, so when you integrate any function, the general solution contains an arbitrary constant. You must include that constant to describe a complete general solution. Many times, you can assume the constant is zero, but to obtain a specific value for the constant, you will usually need either boundary conditions if the problem is spatial, or initial conditions if it is temporal. Adding the constant to the homogeneous solution gives you the particular solution for your problem.

Instructions

- 1
  Write down the general solution equation and the initial conditions or boundary conditions. This helps you see that all the information you need to solve the problem is present.
  Example 1, initial condition: y = sin(t) + C; y = 3 @ t = 0
  Example 2, boundary condition: y = cos(x) + C; y = 6 @ x = 0
- 2
  Enter the initial or boundary condition values and solve the functions.
  Example 1: 3 = sin(0) + C; 3 = 0 + C
  Example 2: 6 = cos(0) + C; 6 = 1 + C
- 3
  Solve the resulting equations algebraically for C.
  Example 1: 3 = 0 + C; C = 3
  Example 2: 6 = 1 + C; C = 5

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