Laplace transform applied to differential equations Guide, Meaning , Facts, Information and Description
The use of
Laplace transform makes it much easier to solve
linear differential equations with given initial conditions.
First consider the following relations:
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Suppose we want to solve the given differential equation:
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This equation is equivalent to
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which is equivalent to
note that the are initial conditions.
Then all we need to get f(t) is to apply the Laplace inverse transform to
An example
We want to solve :
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with initial conditions f(0) = 0 and f ′(0)=0
we note :
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and we get :
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so this is equivalent to :
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we deduce :
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So we apply the Laplace inverse transform and get
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