In this video, we will see two methods with the help of two examples on how to solve differential equations using Laplace transforms if initial conditions are not given at ZERO. Oen way to solve is just keep y(0), y'(0) as it is in the problem and keep on solving but that is not an efficient method. In second method we will see how translations will help us convert the initial value problem which was in y and t variables into the variables u and eta. In this scenario, the initial value problem will become a differential equation with intial condition at ZERO then we solve with our usual method ( https://www.youtube.com/watch?v=Izm5dfYQ8q8 ). ======================================= Links for previous lectures: =================================== Laplace of derivatives when the initial condition is given at ZERO. https://www.youtube.com/watch?v=Izm5dfYQ8q8 =========================== Laplace of Integration https://www.youtube.com/watch?v=uAfggCGCMKE ==================================== The derivative of Laplace i.e., Laplace of t^n f(t) https://www.youtube.com/watch?v=fjJubexPnrY =================== Existence Theorem of Laplace transforms https://www.youtube.com/watch?v=xijkTd0Pc8A ====================================== What are Laplace transforms: https://www.youtube.com/watch?v=Xd_vZzm0AqQ ===================================== Examples on Laplace Transforms: https://www.youtube.com/watch?v=pnSBNpSN030 ====================================== Exponential growth : Concept and Examples: https://www.youtube.com/watch?v=FgqiP4eQ7lo =====================================