← Differential Equations

How to solve

In y = Ce^(kt), setting t = 0 gives y(0) = C directly — the initial value IS the constant.

Steps

  1. Write the general solution y = Ce^(kt).
  2. Substitute t = 0; e⁰ = 1.
  3. So C equals the initial value y(0).

Example

y' = 4y with y(0) = 7. Find C in y = Ce^(4t).

  1. y(0) = C·e⁰ = C.
  2. C = 7.

Answer: 7

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