# 6.021/Notes/2006-09-07

### From OpenWetWare

## Differential Equations

*First order*: no terms of order higher than (such as )

*Linear*: no product of **dependent** variables such as

*Homogenous*: *y* = 0 is a solution

### Solving first-order linear equations

General form:

Solving:

- Find homogenous solution first
- Assume solution is
*y*=*y*_{homo}+*y*_{non − homo}

General solution:

Only three things needed for all such 1st order linear equations: initial value *y*_{0}, final value , time constant τ.

### Example problems

RC circuit, water tank, flux across cell