1.2.3 - Linear Differential Equation
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Practice Questions
Test your understanding with targeted questions
What is the order of the differential equation \( \frac{d^2y}{dx^2} + 5y = 0 \)?
💡 Hint: Look for the highest derivative present.
Identify if the equation \( \frac{dy}{dx} + 4y = 7 \) is linear.
💡 Hint: Check if the dependent variable appears only to the first power.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the general form of a first-order linear differential equation?
💡 Hint: Recall the structure for first-order linear equations.
Is the equation \( y' + 2y = 0 \) linear?
💡 Hint: Check how the dependent variable and its derivative are expressed.
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Challenge Problems
Push your limits with advanced challenges
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.
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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