SME
Differential Equations · Problem type
The steps of solving by Laplace transform
Use this for “Solve y′ + 2y = 6, y(0) = 1, by the Laplace transform.”
Put in order
Put the steps for y′ + 2y = 6, y(0) = 1, in order.
1
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2
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3
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4
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5
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Assumptions
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The transform turns a derivative into algebra: L{y′} = sY − y(0), so the initial value goes in at the start.
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After solving for Y(s), split it into pieces whose inverses are in the table.
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Check the answer: it must satisfy the equation and the initial value.
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