# How do I solve the differential equation #y"-4y'-5y=0# with #y(-1)=3# and #y'(-1)=9#?

##### 1 Answer

As written, there is no solution to the problem.

Definitions: **nth-order differential equation:** a differential equation in which the highest-order derivative presented is of order *n*. Thus, a **first-order differential equation** would involve as its highest-order derivative

**Ordinary differential equation**: a differential equation consisting of a function of one independent variable and its derivatives. An ordinary differential equation might involve

For the work shown below, we assume that

Given the first-order ordinary differential equation above, the first thing we can do is group like terms simplify.

Thus, dividing by -4 and moving terms to opposite sides:

We will first divide both sides by

Recall that

Thus, the initial equation implies a function of the form

We would normally find the constant

Thus, there is no solution to the problem as presented.