Laplace Transforms 5: Example 2y'' + 3y' + y = e^(4t)

Published: 17 December 2023
on channel: Dr. Bevin Maultsby
447
17

(Video 5 of several) We use our previous work that L{y'} = sL{y} - y(0) to find the correct expression for the Laplace Transform of the second derivative: L{y''} = s^2 L{y} - sy(0) - sy'(0). Then we solve a forced second-order differential equation with constant coefficients and initial conditions.

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#mathematics #math #laplace_transformations #laplacetransform #ordinarydifferentialequations #iitjam #iitjammathematics #differentialequations #signalprocessing #HarmonicOscillator


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