ODEs: Find the Laplace Transform of f(t) = t sin(2t). We use the derivative formula for the Laplace Transform: L(y') = sL(y) - y(0) instead of the definition. This method also finds the Laplace transform of g(t) = t cos(2t). We verify the answer by finding the IVP with f(t) as the unique solution.
Dr. Bob explains ordinary differential equations, offering various examples of first and second order equations, higher order differential equations using the Wronskian determinant, Laplace transforms, and more.