Practice Summary (1.10) - Linear Differential Equations - Mathematics (Civil Engineering -1)
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Practice Questions

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Question 1 Easy

Define a first-order linear differential equation.

💡 Hint: Think about the highest derivative involved.

Question 2 Easy

What is an integrating factor?

💡 Hint: Consider how it changes the equation.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What characterizes a linear differential equation?

It includes higher powers of y.
It includes y and its derivatives to the first power.
It has no derivatives.

💡 Hint: Remember the definition of linearity.

Question 2

True or False: An integrating factor is always necessary for solving all first-order linear differential equations.

True
False

💡 Hint: Consider situations where simpler methods apply.

1 more question available

Challenge Problems

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Challenge 1 Hard

Given the non-homogeneous differential equation d²y/dx² - 4y = sin(x), derive the general solution.

💡 Hint: Start by solving the complementary equation before tackling the particular solution.

Challenge 2 Hard

Solve the first-order linear DE dy/dx + 3y = x^2. What steps do you take?

💡 Hint: Don't forget to integrate considering the initial condition if provided.

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