1.5 - Homogeneous Equations with Constant Coefficients
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Practice Questions
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What is the general form of a homogeneous equation?
💡 Hint: Remember it involves derivatives of the function y.
Define what an auxiliary equation is.
💡 Hint: Think of it as the characteristic polynomial derived from the differential equation.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What form does a homogeneous differential equation take?
💡 Hint: Consider the derivatives involved in the equation.
True or false: The roots of the auxiliary equation can be complex.
💡 Hint: Think about the types of solutions we discussed.
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Challenge Problems
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Find the general solution for the differential equation d²y/dx² - 4dy/dx + 4y = 0 and discuss the significance of your results.
💡 Hint: Consider how repeated roots change the form of the solution.
Solve the equation d²y/dx² + 2dy/dx + 5y = 0, derive the general solution and reflect on its application context in engineering.
💡 Hint: Use the quadratic formula on the auxiliary equation to find roots.
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