Practice Ordinary Differential Equation (ode) (18.1.1) - Stability and Convergence of Methods

Practice: Ordinary Differential Equation (ODE)

Lesson 18.1.1Stability and Convergence of Methods

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8 questions

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2 cards from this section. Quick, good the night before a test.
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 main goal of solving an ODE?
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Think about what information is provided in an ODE.
Question 2.
Define 'Initial Condition'.
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Consider how an initial value gives us a starting point.
3Question 3.
What does an ODE involve?
- Only functions
- Functions and their derivatives
- Only derivatives
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Consider what is included in the standard form of an ODE.
4Question 4.
True or False: Initial conditions are not necessary for solving ODEs.
- True
- False
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Think about why we need specific points to solve equations.
Question 5.
Consider the ODE 𝑦' = -2𝑦 with the initial condition 𝑦(0) = 3. Find the explicit solution for 𝑦.
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Recall that this is a first-order linear differential equation; can you solve it using separation of variables or an integrating factor?
Question 6.
Given the second-order ODE 𝑦'' - 5𝑦' + 6𝑦 = 0, find the general solution.
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Consider the characteristic equation formed from the differential equation.

4 more questions in this section. Enroll free to practise them all.