Question
Using the method of undetermined coefficients, find the general solution of the DE
Answer :
Word Count : 381
We are given the differential equation: \[ y^{iv} - 2y'' + 2y'' = 3e^{-x} + 2e^{-x} + \sin x \] ### Step 1: Simplify the differential equation The terms involving \( y'' \) can be combined: \[ y^{iv} = 3e^{-x} + 2e^{-x} + \sin x \] \[ y^{iv} = 5e^{-x} + \sin x \] ### Step 2: Solve the homogeneous equation The homogeneous equation is: \[ y^{iv} = 0 \] The characteristic equation for this is: \[ r^4 = 0 \] This implies \( r = 0 \) with multiplicity 4. Therefore, the general solution ______ __________ _________ _____ ____ ___.
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We are given the differential equation: \[ y^{iv} - 2y'' + 2y'' = 3e^{-x} + 2e^{-x} + \sin x \] ### Step 1: Simplify the differential equation The terms involving \( y'' \) can be combined: \[ y^{iv} = 3e^{-x} + 2e^{-x} + \sin x \] \[ y^{iv} = 5e^{-x} + \sin x \] ### Step 2: Solve the homogeneous equation The homogeneous equation is: \[ y^{iv} = 0 \] The characteristic equation for this is: \[ r^4 = 0 \] This implies \( r = 0 \) with multiplicity 4. Therefore, the general solution ______ __________ _________ _____ ____ ___.
_________ _________ _________ ___ _______ _______ _______ _____ ______ __________ _____ _________.
__________ ______ ________ ___ __________ _________ ___ ______ ______ _______ ____.
______ ___ _____ __________ ____ _________ ______ ______.
_______ _________ ___ _______ __________ _____ ____ ___ _______ __________.
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