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If the initial value problem is and
,y(0)=0 then y(t)=
.
Given the initial value problem be and
,y(0)=0.
We are required to find the solution of the given initial value problem.
Laplace transform is an integral transformation that converts a function of a real variable to a function of a complex variable.
Take laplace on the DE, we get
(Putting the values given in question)
Y(s)=(
Y(s)=1/()
Simplifying the above:
=1/(
=1/[s(s-5)-3(s-5)]
=1/2 [1/(s-3)-1/(s-5)]
Taking inverse of the above we get,
y(t)=
Hence if the initial value problem is and
,y(0)=0 then y(t)=
.
Learn more about laplace transform at brainly.com/question/17062586
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