Q7.3 - 23EExpert-verified
Use Theorem 4 on page362 to show how entry 32 follows from entry 31 in the Laplace transform table on the inside back cover of the text.
It is proved that, from the Laplace transform table.
When specific initial conditions are supplied, especially when the initial values are zero, the Laplace transform is a handy method of solving certain types of differential equations. Laplace transform of a function f(t) is defined as:
In words, we can describe this expression as the Laplace transform of f(t) equals function F of s, that is, .
Consider the expression
Find, using and as:
Hence, it is proved that .
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