Practice Concept Overview: Laplace Transform Of Derivatives (18.3) - Application to Ordinary Differential Equations (ODEs)

Practice: Concept Overview: Laplace Transform of Derivatives

Lesson 18.3Application to Ordinary Differential Equations (ODEs)

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the Laplace transform of the function f(t) = 1?
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Use the definition of Laplace transforms.
Question 2.
What is the first derivative formula in the Laplace transform?
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Recall that it involves the initial value.
3Question 3.
What is the formula for the first derivative in Laplace transforms?
- L{d²f(t)/dt²} = s²F(s)
- L{df(t)/dt} = sF(s) - f(0)
- L{d³f(t)/dt³} = s³F(s)
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Focus on the first-order derivative.
4Question 4.
True or False: The Laplace transform converts initial conditions into algebraic formats.
- True
- False
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Think about how initial conditions are integrated.
Question 5.
Using Laplace transforms, solve the ODE d³y/dt³ + 5d²y/dt² + 6dy/dt = 0 with initial conditions y(0)=2, y'(0)=1, y''(0)=0.
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Factoring the polynomial in the s-domain will give you a better insight.
Question 6.
Determine the Laplace transform of f(t) = t^2e^(-3t) and find its first derivative using this approach.
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You may need to use differentiation under the integral sign.

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