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Using laplace transform find function y given 2nd derivative of y plus y equals 0 with both initial conditions equal to 0?
Wiki User
∙ 11y ago
Solve y''+y=0 using Laplace.
Umm y=0, 0''+0=0, 0.o Oh well here it is.
First you take the Laplace of each term, so . . .
L(y'')+L(y)=L(0)
Using your Laplace table you know the Laplace of all these terms
s2L(y)-sy(0)-y'(0) + L(y) = 0
Since both initial conditions are 0 this simplifies to. . .
s2L(y) + L(y) = 0
You can factor out the L(y) and solve for it.
L(y) = 0/(s2+1)
L(y) = 0
Now take the inverse Laplace of both sides and solve for y.
L-1(L(y)) = L-1(0)
y = 0
Wiki User
∙ 11y ago
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