Extracted text: The radiofrequency, y detected from the transmitter of a wireless microphone varies...

Question

Extracted text: The radiofrequency, y detected from the transmitter of a wireless microphone varies with respect to
the distance, x from the source in the following manner:
,"+2 y'+5 y = 5x² +12
(a)
Produce the complementary solution, y of the above differential equation.
(b)
Produce the particular solution, y̟ of the above differential equation.
(c)
Hence, state the complete solution modelling the radiofrequency detected.

Aditi · Accepted Answer

SOLUTION
y'' +2y' + 5y = 5x 2 + 12
y(D2 +2D +5)= 5x2 + 12
CF => D2+ 2D + 5 = 0
a = 2 , b = 5 
d = a2 - 4b = 4 - 20 = - 16
k = 1/2 * √ d = 1/2 * √ - 16
k = 4i/2
k = 2i
Complementary solution:

The radiofrequency, y detected from the transmitter of a wireless microphone varies with respect to the distance, x from the source in the following manner: ,"+2 y'+5 y = 5x² +12 (a) Produce the...

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