(B) Given the differential equation: $x \frac{dy}{dx} - y = 0$ Rearranging the terms,we get: $x \frac{dy}{dx} = y$ Separating the variables: $\frac{dy

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(B) Given the differential equation: $x \frac{dy}{dx} - y = 0$ Rearranging the terms,we get: $x \frac{dy}{dx} = y$ Separating the variables: $\frac{dy}{y} = \frac{dx}{x}$ Integrating both sides: $\int \frac{dy}{y} = \int \frac{dx}{x}$ This gives: $\ln|y| = \ln|x| + \ln|c|$ Using the property of logarithms: $\ln|y| = \ln|cx|$ Taking the exponential of both sides: $y = cx$ Thus,the correct option is $B$.

Class 12 Mathematics Differential Equations Variable separable type differential equations

Easy

The solution of the differential equation $x \frac{dy}{dx} - y = 0$ is . . . . . . .

GSEB 2020 All GSEB

A
$e^x y = c$
B
$y = cx$
C
$x = cy$
D
$e^{xy} = c$

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