Use the laplace transform to solve y4ygt y0 1 y00 gtt t2 5...

Transcript

00:01 Dear students here we have a question and we have to use laplace transformation to solve this this initial value problem here the initial conditions are y of 0 is equal to zero and y prime of zero is equal to zero so let's apply laplace on each of the term it will be laplace y double prime plus four laplace y prime plus five laplace of y is equal to laplace of daba into it is del into t minus so dear students here we know that here we know that the plus of y double prime it is y double prime deuce it is double prime is double prime is equal to s square y of s y of s minus s y of zero minus y prime of zero and here here we have leplas of y prime is equal to s it is not s squared it is s it is y of s is s y of s minus y of zero so dear students here notice that we have y of zero and y prime of zero is equal to zero so we're putting these values the formula will become the formula will become to be s squared y of s plus 4 s y of s and for this one it will be plus 5 y of s y of s y of s you said it is y of y of s is equal to and we know that laplace of delta into t minus a is equal to what it is equal to e to the power e to the power minus a s here in our perspective a is but it is 2 pi so it will be e to the power minus 2 pi s so these students now taking y of s command to be y of s is equal to and it will be it will be it will be just 20 to be y of s into y of s into s square plus 4 s plus 5 is equal to e to the power minus 2 pi s so now these students y of s will be equal to e to the power minus 2 pi s divided by s square plus 4 s plus if we will if we will make it as dear students let's say it will be it will be let's it is what it is 5 so so this now applying now applying dear students now applying now applying now applying the now applying the now applying the laplace inverse of y of s is equals to is equal to leplas inverse of e to the power minus 2 by s divided by here we have this will be equal to this will be equal to e to the power it will be equal to s square minus 4 s this plus 4 plus plus plus four plus one we have these students we here we have we have we have here we have these students breakdown five…

Question

use the Laplace transform to solve: y''+4y=g(t); y(0)=-1, y'(0)=0, g(t)={[t, t<2; 5, t>2]

Question

use the Laplace transform to solve: y''+4y=g(t); y(0)=-1, y'(0)=0, g(t)={[t, t<2; 5, t>2]

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