Page 64 - LAPLACE TRANSFORM

4.0 DIFFERENTIAL EQUATIONS

4.1 First order differential equation

Differential Equations

The Laplace transform can simplify the solution of problems involving differential
equations.

Time domain Frequency domain

x X(s)

y Y(s)

A

5
-2t
5e
( + 2)
10
3t
10e
( − 3)

f’(t) = s F(s) – f (0) ; f (0) when t=0

dx
= x’(t) = s X(s) – x (0) ; x (0) when t=0
dt

dy
= y’(t) = s Y(s) – y (0) ; y (0) when t=0
dt

Example 1

By using Laplace Transform, calculate the time domain x(t) for the given function.

dx
– 4x = 8 ; given x (0) =2
dt

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