Practice Steps to Solve Using Laplace Transforms - 17.4.2 | 17. Application to Simultaneous Linear Differential Equations | Mathematics - iii (Differential Calculus) - Vol 1
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17.4.2 - Steps to Solve Using Laplace Transforms

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the first step in solving simultaneous linear differential equations with Laplace Transforms?

💡 Hint: Think about what transforms initial conditions.

Question 2

Easy

What do we call the function we get after applying the Laplace Transform?

💡 Hint: It’s what we manipulate to find solutions!

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the primary benefit of using Laplace Transforms on differential equations?

  • Makes equations longer
  • Converts to algebraic form
  • Avoids initial conditions

💡 Hint: Consider how it helps with the solution process.

Question 2

True or False: The Inverse Laplace Transform is used to return to the time domain.

  • True
  • False

💡 Hint: Recall our discussion about time-domain solutions.

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Challenge Problems

Push your limits with challenges.

Question 1

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.

💡 Hint: Remember the substitution principle for simultaneous equations.

Question 2

Demonstrate an example where the Laplace Transform fails, such as a non-linear differential equation, and discuss why this is the case.

💡 Hint: Think back to the conditions under which Laplace is applicable.

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