(C) Given differential equation is,$\frac{dy}{y} + \frac{dx}{x} = 0$.Integrating both sides with respect to their variables:$\int \frac{dy}{y} + \int

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(C) Given differential equation is,$\frac{dy}{y} + \frac{dx}{x} = 0$.Integrating both sides with respect to their variables:$\int \frac{dy}{y} + \int \frac{dx}{x} = \int 0 \, dx$Using the standard integral formula $\int \frac{1}{u} du = \log |u| + C$,we get:$\log |y| + \log |x| = \log |c|$Using the logarithmic property $\log a + \log b = \log(ab)$:$\log |xy| = \log |c|$Taking the exponential on both sides:$xy = c$

Class 12 Mathematics Differential Equations Variable separable type differential equations

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The solution for the differential equation $\frac{dy}{y} + \frac{dx}{x} = 0$ is:

KCET 2016 All KCET

A
$\frac{1}{y} + \frac{1}{x} = C$
B
$\log x \cdot \log y = c$
C
$xy = c$
D
$x + y = c$

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