Differential equations are often difficult to solve because they involve unknown functions entangled with their derivatives. This complexity grows when the equation involves discontinuities or initial conditions. The Laplace Transform simplifies this process by converting the differential equation into an algebraic form, making it easier to solve. One of the key motivations for using the Laplace Transform is its ability to handle these discontinuities seamlessly, transforming functions piecewise into a single, continuous function in the complex plane. Through this, we can solve problems that would otherwise be very challenging with traditional methods.
