3.2 - Characteristic Equation
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Practice Questions
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What is the characteristic equation derived from the equation d²y/dx² - 3dy/dx + 2y = 0?
💡 Hint: Only consider the coefficients of the original equation.
What happens when the discriminant is negative?
💡 Hint: Think about how the roots can affect the solution's behavior.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the characteristic equation derived from d²y/dx² + 2dy/dx + y = 0?
💡 Hint: Look carefully at how the differential equation coefficients correspond to terms in the characteristic equation.
If the discriminant is zero, what type of roots do we have?
💡 Hint: Think about what this implies for the general solution.
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Challenge Problems
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Derive the general solution for the ODE d²y/dx² - 6dy/dx + 9y = 0.
💡 Hint: Use the quadratic formula and remember the implications of multiple roots.
For the differential equation y'' + 4y' + 20y = 0, find and analyze the nature of its roots and the general solution.
💡 Hint: Identify the real and imaginary parts carefully to construct the final solution.
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