# EE102 Systems and Signals (Discussion)

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Next: Constant Coefficients Up: First Order Linear Differential Previous: First Order Linear Differential

## General Case

The general first-order linear differential equation is given by:

where a(t) and x(t) are given functions, and we need to solve for for given the initial condition .

To solve the equation for , we use the well-known trick of multiplying the equation by the so-called integrating factor:

This gives:

But by the product rule of differentiation, the LHS is

since

(product rule)

and

Hence, the differential equation now becomes:

To get , we first change the to and integrate from 0 to :

The integral on the LHS is just . Therefore, using the initial condition , we get

Finally, rearranging terms, we get the solution to be

Next: Constant Coefficients Up: First Order Linear Differential Previous: First Order Linear Differential

visitors since January 7., 2002. -

Sankaran Panchapagesan
2002-06-05