GATE (TF) Textile 2022 Question Paper Solution | GATE/2022/TF/03

Question 3 (Textile Technology & Fibre Science)

An integrating factor of the differential equation
xdy + (1-y)dx = 0 is

(A)\frac{1}{x}
(B)x
(C)e^x
(D)\frac{1}{x^2}
[Show Answer]

xdy + (1-y)dx = 0

or
Devided by x dx both side-

\frac{dy}{dx}+\frac{1-y}{x}=0

\frac{dy}{dx}+\frac{-1}{x} \times y=\frac{-1}{x}

\frac{dy}{dx}+Py=Q

Where P and Q are the funtion x.

And

Integrating factor=e^\int (P dx)

Where, P=\frac{-1}{x}

Integrating factor=e^\int (\frac{-1}{x} \times dx)

Integrating factor=e^(-log x )

Integrating factor=e^(log\frac{1}{x})

Integrating factor=\frac{1}{x} (Ans)

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