Using the method of variation of parameters, solve the differential equation:

To solve the given differential equation using the method of variation of parameters, we first need to solve the associated homogeneous equation:

\[ \frac{d^2y}{dx^2} + y = 0 \]

The solution to this equation is \( y_h = c_1 \cos x + c_2 \sin x \), where \( c_1 \) and \( c_2 \) are arbitrary constants.

Now, for the particular solution \( y_p \), we assume:

\[ y_p = u_1(x) \cos x + u_2(x) ______ _____ ________ ______ _______ _________.
__________ _____ ___ ________ _________ _______ ________ _____ ____ _________ _____ ___.
____ ___ ____ ___ _____ __________ _______ ___.
____ _________ ________ __________ ______ ___ ______ _____ _________ _________ ___.
_______ ______ ______ _______ ________ _______ _____ ___ _________ ______ _______ _________.
____ _____ _____ ____ ____ ____ ___ __________ _________ _________ ___ ____.
____ ______ ____ ________ ____ _________ _____ ___ ______ _____.
_________ ___ ____ ________ _________ _______ _____ ________.
______ ________ ________ ____ ________ _____ _________ ____ ________ ________ ___ _____.
________ ___ ____ ______ _________ ________ _________ ____ __________ _____.
__________ ________ __________ _______ ___.
__________ _______ ____ ________ ________ ______ _______ ___ ____.
________ ___ _____ _________ ____ __________.
____ _________ _____ ___ _________ ___ _______ ________ ____ _________ ___.
____ __________ ______ ______ _________ _______ ___ _____ _______ _______ ___.
_______ _______ _____ _____ ______ ___.
________ _____ ___ __________ _____ ______.
________ ______ ________ _____ _____ _____ _____.
__________ _________ ______ ____ ________ ________ ___ ___ ____ ________ ____.
____ _____ _______ ___ ______ _______ _____ __________ ________ ____ __________.
________ ____ _____ ______ _______ ____ __________ _________.
________ ________ ____ ____ _____ __________ _________ _______ __________.
__________ __________ _____ ________ __________.
________ ______ ________ _______ _______ ____ ______ __________ ________ ____.
________ _____ ______ _________ ___ _________.
_________ ________ _____ __________.
Get Full Answer on WhatsApp