Practice Linear Differential Equation (1.2.3) - Linear Differential Equations

Practice: Linear Differential Equation

Lesson 1.2.3Linear Differential Equations

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8 questions

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6 sample questions

Question 1.
What is the order of the differential equation $\frac{d^2y}{dx^2} + 5y = 0$ ?
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Look for the highest derivative present.
Question 2.
Identify if the equation $\frac{dy}{dx} + 4y = 7$ is linear.
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Check if the dependent variable appears only to the first power.
3Question 3.
What is the general form of a first-order linear differential equation?
- \$ y + P(x) = Q(x) \$
- \$ \\frac{dy}{dx} + P(x)y = Q(x) \$
- \$ \\frac{dy}{dx} = P(x) + Q(x) \$
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Recall the structure for first-order linear equations.
4Question 4.
Is the equation $y' + 2y = 0$ linear?
- True
- False
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Check how the dependent variable and its derivative are expressed.
Question 5.
Given the equation $y''' + 9y = 0$ , identify its order and classify if it is linear or not.
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Identify the highest derivative to find the order.
Question 6.
Classify the equation $\frac{d^2y}{dt^2} + 3 \frac{dy}{dt} + 2y = e^t$ . Determine its order and if it's homogeneous.
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Check the right-hand side for non-homogeneity.

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