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\nLinear Second-Order Differential Equations Part 1: Homogeneous Case\n

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\n\nPublisher:\n\nProfessor Dave Explains\n\n\n
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\nAfter a number of tutorials covering first-order differential equations, it's time to start tackling second-order differential equations. These contain a second derivative term, and they are quite useful in physics. To introduce these,...\nAfter a number of tutorials covering first-order differential equations, it's time to start tackling second-order differential equations. These contain a second derivative term, and they are quite useful in physics. To introduce these, let's first examine the simplest case, a linear homogenous second-order differential equation that exhibits constant coefficients. To solve these we will need to find a characteristic equation and do some algebra, a process which will vary depending on whether we are dealing with real distinct roots, complex roots, or a repeated root. Let's take a look!\n
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Media Length
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9:49
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Grade
9th - Higher Ed
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Subjects
Math
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\nProfessor Dave Explains\n\n
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Date
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2025
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English
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For Teacher Use
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Concepts

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complex roots, coefficients, roots, velocity, solutions
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Additional Tags

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second order differential equations, homogenous second order differential equations, constant coefficients case, characteristic equation, auxiliary equation, ansatz solution, superposition principle, linear independence, initial value problem, boundary value problem, simple harmonic motion, dx squared, linear homogeneous, repeated root, quadratic equation, general solution, constant coefficients, times cosine, times sine, boundary conditions, lambda 2x, solution, superposition, times, derivative, newton, form, fact, dashpot, damped, oscillations, lambda, lambda 2, rate
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\n\" data-title=\"Get Full Access\" data-container=\"body\" rel=\"popover\" tabindex=\"0\" aria-label=\"Play video: Linear Second-Order Differential Equations Part 1: Homogeneous Case\" href=\"/subscription/new\">\"Linear\n\n
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