GATE (TF) Textile 2016 Question Paper Solution | GATE/2016/TF/29

Question 29 (Textile Engineering & Fibre Science)

The integrating factor of $(2 \cos y + 4x^2)dx -x\sin y \:dy = 0$ is

(A)	$-x$
(B)	$x$
(C)	$x^2$
(D)	$-x^2$

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$(2 \cos y + 4x^2)dx -x\sin y \:dy = 0$
$x siny \frac{dy}{dx}-2cos y=4x^2$
Let cosy=t
$-siny \frac{dy}{dx}=\frac{dt}{dx}$
$\frac{dt}{dx}+\frac{2}{x} t=-4x$
Now,
Integrating fractor= $e^\int {P dx}$
P= $\frac{2}{x}$
Integrating fractor= $e^\int {\frac{2}{x}dx}$
Integrating fractor= $e^2log x$
Integrating fractor= $e^{log x^2}$
Integrating fractor= $x^2$

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