Practice Solving Differential Equations - 1.2.1 | 5. Laplace Transform of Derivatives | Mathematics - iii (Differential Calculus) - Vol 1
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Solving Differential Equations

1.2.1 - Solving Differential Equations

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the formula for the Laplace Transform of the first derivative?

💡 Hint: Recall the components: the transform of the original function and its initial value.

Question 2 Easy

Define an Initial Value Problem (IVP).

💡 Hint: Focus on what needs to be known before solving.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the result of L{f'(t)}?

sF(s) + f(0)
sF(s) - f(0)
sf(0) - F(s)

💡 Hint: Think about how derivatives relate to the function itself.

Question 2

True or False: The second derivative transforms to L{f''(t)} = s^2F(s) - sf(0)

True
False

💡 Hint: Recall the formula and check for omissions.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Solve the differential equation y''' + y'' + 2y' + y = 0 using Laplace Transforms.

💡 Hint: Identify the characteristic equation formed by the s-domain.

Challenge 2 Hard

For the function f(t) = t^2e^(2t), calculate its Laplace Transform directly.

💡 Hint: Look up how polynomial functions behave under transforms!

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Reference links

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