Practice Example - 1.3.3 | 1. Linear Differential Equations | Mathematics (Civil Engineering -1)
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Example

1.3.3 - Example

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Practice Questions

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Question 1 Easy

What is the form of a first-order linear differential equation?

💡 Hint: Look for terms involving dy/dx, a function of y, and a separate function.

Question 2 Easy

Identify P(x) from the equation dy/dx + 2y = e^(-x).

💡 Hint: It's the coefficient of y in the equation.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the purpose of the integrating factor in differential equations?

To simplify the right side
To combine terms
To rewrite the equation as an exact derivative

💡 Hint: Think about what converting the equation into an exact derivative means.

Question 2

True or False: The integrating factor is always e^(∫P(x) dx).

True
False

💡 Hint: Recall how we derived the integrating factor.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Solve the equation dy/dx + 4y = sin(x).

💡 Hint: Consider the integration techniques for sin(x)e^(4x).

Challenge 2 Hard

Derive the general solution to the differential equation dy/dx + 5y = 3e^(3x).

💡 Hint: Remember to simplify your final answer.

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