15.14 - Laplace Transform in Solving Differential Equations
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Practice Questions
Test your understanding with targeted questions
What is the general form of a second-order linear ODE?
💡 Hint: Look for coefficients and derivatives in the equation.
What does the Laplace Transform do?
💡 Hint: Think about transformations that simplify solving equations.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the Laplace Transform of y''?
💡 Hint: Focus on how derivatives are represented in the transform.
True or false: The Laplace Transform can only be applied to periodic functions.
💡 Hint: Think about the broader applicability of the transform in different conditions.
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Challenge Problems
Push your limits with advanced challenges
Consider the equation y'' + 4y = sin(t), with initial conditions y(0) = 1 and y'(0) = 0. Apply the Laplace Transform and find Y(s).
💡 Hint: Focus on how sin(t) transforms and how to handle initial values.
Find the inverse Laplace Transform of Y(s) = 5/(s^2 + 1).
💡 Hint: Remember the transformation pairings for sine functions.
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