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Question Number 78105 by aliesam last updated on 14/Jan/20

	Answered by Kunal12588 last updated on 14/Jan/20

	$\frac{d y}{d x} + (t a n x) y = s i n 2 x$ $T h i s i s a l i n e a r d i f f e r e n t i a l e q u a t i o n$ $d i f f e r e n t i a l e q u a t i o n o f t h e t y p e$ $\frac{d y}{d x} + P x = Q; P & Q a r e f u n c t i o n o f x o n l y$ $P = t a n x, Q = s i n 2 x$ $I . F . = e^{\int P d x}$ $\Rightarrow I . F . = e^{\int t a n x d x}$ $\Rightarrow I . F . = e^{l o g ∣ s e c x ∣} = s e c x$ $s o l u t i o n o f d i f f e r e n t i a l e q u a t i o n$ $y (I . F) = \int (I . F) \times Q d x$ $\Rightarrow y s e c x = \int s e c x 2 s i n x c o s x s x$ $\Rightarrow y s e c x = 2 \int s i n x d x$ $\Rightarrow y s e c x = - 2 c o s x + C$ $\Rightarrow y = - 2 {c o s}^{2} x + C c o s x$
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