Imagine turning a differential equation into an algebra problem instead. Thatβs exactly what the Laplace transform method does. It unfolds in the same three steps:
Backward transform. Apply the inverse Laplace transform to the prepared \(Y(s)\) to turn it back into \(y(t)\) as the solution to the origianl differential equation.
Once transformed, solve for \(Y(s)\) and prepare it for the inverse transform with techniques such as partial fraction decomposition and completing the square.
