Homework SourseFind the Laplace transform of the solution to the initial va
Find the Laplace transform of the solution to the initial value problem
y(double prime) - 2y(prime) + 6y = 0; y(0) = 2, y(prime)(0) = 3.
y(double prime) - 2y(prime) + 6y = 0; y(0) = 2, y(prime)(0) = 3.
Solution
we have, y\'\' - 2y\' + 6y = 0 taking lapalce transform, [ s^2 Y(s) - s y(0) - y\'(0) ] - 2 [ sY(s) - y(0)] + 6 Y(s) = 0 [ s^2 Y(s) - 2s - 3 ] - 2 [ sY(s) -2] + 6 Y(s) = 0 Y(s) [ s^2 - 2s + 6 ] = [ 2s - 1] Y(s) = [ 2s - 1]/ [ s^2 - 2s + 6 ]
