Practice Linear Differential Equation - 1.2.3 | 1. Linear Differential Equations | Mathematics (Civil Engineering -1)
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Linear Differential Equation

1.2.3 - Linear Differential Equation

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the order of the differential equation \( \frac{d^2y}{dx^2} + 5y = 0 \)?

💡 Hint: Look for the highest derivative present.

Question 2 Easy

Identify if the equation \( \frac{dy}{dx} + 4y = 7 \) is linear.

💡 Hint: Check if the dependent variable appears only to the first power.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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) \\)

💡 Hint: Recall the structure for first-order linear equations.

Question 2

Is the equation \( y' + 2y = 0 \) linear?

True
False

💡 Hint: Check how the dependent variable and its derivative are expressed.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the equation \( y''' + 9y = 0 \), identify its order and classify if it is linear or not.

💡 Hint: Identify the highest derivative to find the order.

Challenge 2 Hard

Classify the equation \( \frac{d^2y}{dt^2} + 3 \frac{dy}{dt} + 2y = e^t \). Determine its order and if it's homogeneous.

💡 Hint: Check the right-hand side for non-homogeneity.

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