9. The solution of the equation x \frac{d y}{d x}+y=0 passing through the point (1,1) is

GATE Civil Engineering (CE) 2018 Shift 2 Solved Paper

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9. The solution of the equation

x \;{d y}/{d x}+y=0

passing through the point

(1,1)

Solution:

x \;{d y}/{d x}+y \;\; =0

x \;{d y}/{d x} \;\; =-y

\;{d y}/{y} \;\; =-\;{d x}/{x}

∫ \;{1}/{y} d y \;\; =∫ \;{-1}/{x} d x

In y \;\; =-In x+c

When

y=1, x=1

c=0

⇒ \;\; y=\;{1}/{x}=x^{-1}

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