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3 cards from this section. Quick, good the night before a test.
Solve the equation d²y/dx² - 2dy/dx + y = 0.
Look for repeated roots in the auxiliary equation.
Solve the equation d²y/dx² + 4y = 0.
Check for complex roots in the auxiliary equation.
What is the general solution of d²y/dx² - 5dy/dx + 6y = 0?
Derive it from the auxiliary equation.
True or False: The general solution for repeated roots includes a linear term.
Recall the formula for repeated roots.
Solve the differential equation d²y/dx² - 8dy/dx + 16y = 0 and analyze the implications of the solution.
Pay attention to the nature of the roots and apply the correct form.
Evaluate the equation d²y/dx² + 6dy/dx + 10y = 0, identify the nature of the roots, and provide the general solution.
Utilize the quadratic formula and consider the implications of complex roots.
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