This is a two-part question. (a) The correct form for the partial fraction decomposition of 4+5+45 04+ 5+05 4+B+5 2s2-128-40 $3-582 10 8-1 8+2 is (b) The Laplace transform of the solution f(t) of an initial value problem is given by 27e-5s 82+9 By taking the inverse of the Laplace transform find and the enter the function f(t) below in maple syntax. f(t) =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve both parts. Thank you!

Need only handwritten solution only (not typed one).

We can apply Laplace transform to an ODE in t with given initial values to form an algebraic equation in F(s),
the Laplace transform of the solution. Then we solve the equation to get the Laplace transform of the solution.
Finally, we apply the inverse Laplace transform to get the solution of the IVP.
This question is on the second half of the process. We first resolve F(s) into partial fractions, then apply the
inverse Laplace transform to get the solution of the IVP.
This is a two-part question.
(a) The correct form for the partial fraction decomposition of
04+1/2+ 8+5
A+B
A + B +
+
8+5
8-5
8-5
2s2-128-40
$3-582
10
is
(b) The Laplace transform of the solution f(t) of an initial value problem is given by
8 27e-5s
s+2 $2+9
By taking the inverse of the Laplace transform find and the enter the function f(t) below in maple syntax.
f(t) =
Transcribed Image Text:We can apply Laplace transform to an ODE in t with given initial values to form an algebraic equation in F(s), the Laplace transform of the solution. Then we solve the equation to get the Laplace transform of the solution. Finally, we apply the inverse Laplace transform to get the solution of the IVP. This question is on the second half of the process. We first resolve F(s) into partial fractions, then apply the inverse Laplace transform to get the solution of the IVP. This is a two-part question. (a) The correct form for the partial fraction decomposition of 04+1/2+ 8+5 A+B A + B + + 8+5 8-5 8-5 2s2-128-40 $3-582 10 is (b) The Laplace transform of the solution f(t) of an initial value problem is given by 8 27e-5s s+2 $2+9 By taking the inverse of the Laplace transform find and the enter the function f(t) below in maple syntax. f(t) =
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