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

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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
Integrating fractor=e^\int {P dx}
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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