Apply the method of variation of parameter to solve the differential e

Question

Apply the method of variation of parameter to solve the differential equation:

$$y'' + 6y' + 9y = \frac{1}{x^3} e^{-3x}, \quad x > 0.$

09 Jan 2026

Answer :

Word Count : 304

The given differential equation is: [ y'' + 6y' + 9y = \frac{1}{x^3} e^{-3x}, \quad x>0 ] The associated homogeneous equation is: [ y_h'': y'' + 6y' + 9y = 0 ] The characteristic equation is: [ r^2 + 6r + 9 = 0 ] [ (r + 3)^2 = 0 \implies r = -3 \text{ (repeated root)} ] So ___ ___ ________ _______ ________ _____ ______ _______ __________.
_________ _________ _______ ____ __________ _______ ____ _________ _______ ____ _____.
____ ___ ____ ________ ______ ________ _________ ____ ___.
________ ________ __________ _______ ______ _________ _________ ____ ________ _____ ____ ___.
_____ __________ ___ _________ _______ _________ ___ ________ _________ _______ ______ _________.
_________ ___ ____ ___ __________ _______ ____ __________ _______ ______ _______.
_______ _____ _____ ___ _________ ____.
_____ ____ ______ _______ _________ ______ __________ _______ _____ ________ ___.
___ _________ ___ _________ ____ ___ ___ _____ __________.
___ _____ _________ __________ ___ _______.
__________ ________ _______ ____ ________ ______ _____ _______ _________ ____ _______ __________.
_________ ______ __________ _________ ________ _________ _________ _______ _________.
_________ ___ ____ _____ ___ ______ _____.
___ ________ ______ ________ __________ ____ ___.
____ _________ _____ ___ _________.
___ ________ _________ ___ _________.
____ ____ _________ ___ _________ __________ ____.
__________ _________ ____ _________ ______ _________.
____ _______ __________ ________ ________ ___ _______ ______ _____.
_______ _______ _________ _____ ________ _______ ____ _____ __________ __________.
_________ ___ ________ ________ ______ ___ __________ ______ _____ ______.
____ ___ ________ ___ ______ _______ _________ _________ _________ _____ ________ _____.
_____ _________ ____ ______ _____ __________ ________ ________ _______ _______ ______.
___ _______ _____ ____ ________ _________ _________ ____ ____ ________ ______ _______.
___ ________ ________ _______ ____ ___ _____ ______ __________.
____ ________ ____ _______ _________ ______ _____ _______ ______ ______.
__________ ___ ___ _________ ________ ________.
____.
Get Full Answer on WhatsApp

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers

IGNOU NEWS

Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★