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Find a particular solution to
y′′+5y′+6y=10te⁴ᵗ yₚ=

User Fiw
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1 Answer

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Final answer:

To find a particular solution for the differential equation y''+5y'+6y=10te^4t, assume a solution of the form y_p = Ate^4t, substitute it into the equation, and solve for the constant A to obtain y_p.

Step-by-step explanation:

To find a particular solution to the second-order linear nonhomogeneous differential equation y''+5y'+6y=10te4t, we look for a solution of the form yp = Ate4t where A is a constant that needs to be determined. First, plug in yp and its derivatives into the differential equation.

After substituting and simplifying, you can solve for A by collecting like terms and equating coefficients. This will give you the particular solution yp.

User Cesarina
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