Question

Solve the nonhomogeneous differential equation y′′+6y′−16y=e5x. Find the most general solution to the associated homogeneous differential equation. Use c1 and c2 in your answer to denote arbitrary constants, and enter them as c1 and c2. yc= c1e^(-8x)+c2e^(2x) help (formulas) Using the Method of Undetermined Coefficients, give the form of a particular solution needed to solve this differential equation. Use capital letters A, B, C, etc. for the unknown coefficients, starting with A. yp= Ae^(5x) help (formulas) Find a particular solution to this nonhomogeneous differential equation. yp= 1/39e^(5x) help (formulas) Find the most general solution to the original nonhomogeneous differential equation. Use c1 and c2 in your answer to denote arbitrary constants. y= c1e^(-8x)+c2e^(2x)+1/39e^(5x) help (formulas) Find the solution to the original nonhomogeneous differential equation satisfying the initial conditions y(0)=−2 and y′(0)=2. y= -17/78e^(-8x)+141/78e^(2x)+1/39e^(5x) help (formulas)

Answer 1

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