CH ENGR 102A Lecture 1: Solving Linear ODEs using Laplace Transforms
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Solving linear ode using laplace transforms y y. This is a linear homogeneous ode and can be solved using standard methods. L y t y s , we inverse transform to determine ( ) Once we find ( ) y s . , we derive a new equation for y s . The first step is to take the laplace transform of both sides of the original differential equation. Obviously, the laplace transform of the function 0 is 0. Using linearity of the inverse transform, we have y t. In the direct approach one solves for the homogeneous solution and the particular solution separately. For this problem the particular solution can be determined using variation of parameters or the method of undetermined coefficients. Laplace transform technique we can solve for the homogeneous and particular solutions at the same time. Let y s be the laplace transform of ( )y t of the differential equation we have:
