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Consider the second-order equation d2y dt2 + 5dy dt +

6y = 0, 1. Convert the equation to a first-order, linear system,

User Ncerezo
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Final answer:

To convert the second-order differential equation into a first-order system, a new variable v is defined as dy/dt, resulting in a system of two first-order equations: dv/dt = -5v - 6y and dy/dt = v.

Step-by-step explanation:

To convert the second-order differential equation d2y/dt2 + 5dy/dt + 6y = 0 into a first-order linear system, we introduce a new variable to reduce the order of the differential equation. Let's create a variable called v such that v = dy/dt. This allows us to rewrite the original second-order equation in terms of v and y.

The system of first-order equations will be:



This first-order system can be represented in matrix form or solved using methods for systems of first-order linear differential equations.

User TjerkW
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