# Initial Value Problems

- Author:
- Ken Schwartz

The Initial Value Problems (IVPs) that we will study are essentially just antiderivatives with an initial condition applied, which allows us to obtain the value of " ", the constant of integration.
Until we are given an initial condition (a point on the solution curve), we cannot determine the value of , and so the general solution is really an infinitely-large family of curves, one curve for each value of .

We write the equation as a Differential Equation (using a derivative):
We then take the antiderivative of both sides, combining the two constants into one on the right side:
This gives us the ", giving us the

**. Finally, we apply the initial condition to obtain "***general solution***.***particular solution*