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3 cards from this section. Quick, good the night before a test.
What is the first step in solving simultaneous linear differential equations with Laplace Transforms?
Think about what transforms initial conditions.
What do we call the function we get after applying the Laplace Transform?
It’s what we manipulate to find solutions!
What is the primary benefit of using Laplace Transforms on differential equations?
Consider how it helps with the solution process.
True or False: The Inverse Laplace Transform is used to return to the time domain.
Recall our discussion about time-domain solutions.
Consider a system where dx/dt = 5y - 6x and dy/dt = 3x + 5y. With initial conditions x(0)=2, y(0)=1, solve this using Laplace Transforms and back-substitution. Show every step.
Remember the substitution principle for simultaneous equations.
Demonstrate an example where the Laplace Transform fails, such as a non-linear differential equation, and discuss why this is the case.
Think back to the conditions under which Laplace is applicable.
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