ODEs
An ordinary differential equation is an equation of the following:
An ODE is called separable if it can be written as
and is readily solved by integration of each side
As a specific case where , we have . This is a specific case of a linear, homogenous equation. An ODE is linear if it can be written as
In the inhomogeneous case, it can be solved by the method of integrating factors:
1. Multiply each side by
2. Applying the product and chain rules
3. Integrate each side and solve by applying FTC