2.5.1 - Solving Differential Equations
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Practice Questions
Test your understanding with targeted questions
Find the Laplace Transform of f(t) = 2t + 3.
💡 Hint: Remember to apply linearity and find the transforms of each part.
What is the Laplace Transform of f(t) = sin(t)?
💡 Hint: Refer to the formula for sine.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the Linearity Property state?
💡 Hint: Think about how we can handle combinations of functions.
True or False: The Laplace Transform can only be applied to single functions.
💡 Hint: Recall how we apply transformations to multiple functions.
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Challenge Problems
Push your limits with advanced challenges
Given f(t) = 5t + 3cos(t) and g(t) = 2t² + sin(2t), find ℒ{f(t) + g(t)}.
💡 Hint: Break it down using known transforms!
Prove the dependency on linearity by applying the Laplace Transform to a third-order equation involving constant coefficients.
💡 Hint: Recall definitions of derivatives and transforms.
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