d-2-a-2-y-tan-ax-by-the-method-of-variation-of-parameters-

Question Number 47035 by 23kpratik last updated on 04/Nov/18

(d^{2} + a^{2}) y = t a n a x b y t h e m e t h o d o f v a r i a t i o n o f p a r a m e t e r s

Commented by tanmay.chaudhury50@gmail.com last updated on 04/Nov/18

p l s c l a r i f y d m e a n s \frac{d}{d x} i s i t \dots

Answered by tanmay.chaudhury50@gmail.com last updated on 05/Nov/18

y = \frac{1}{D^{2} + a^{2}} t a n a x

= \frac{1}{D^{2} + a^{2}} \times \frac{2 i s i n a x}{i \times 2 c o s a x}

= \frac{1}{D^{2} + a^{2}} \times \frac{e^{i a x} - e^{- i a x}}{i \times (e^{i a x} + e^{- i a x})}

e^{i a x} = c o s a x + i s i n a x

e^{- i a x} = c o s a x - i s i n a x

y = \frac{1}{(D + i a) (D - i a)} \times \frac{1}{i} \times \frac{e^{i 2 a x} - 1}{e^{i 2 a x} + 1}

= w a i t \dots