The solution of frac{dy}{dx} = frac{1}{x} is | vedclass

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(B) Given the differential equation: $\frac{dy}{dx} = \frac{1}{x}$.To solve this,we use the method of separation of variables.Separate the variables $

Vedclass · Accepted Answer

$y = \log x + c$

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(B) Given the differential equation: $\frac{dy}{dx} = \frac{1}{x}$.To solve this,we use the method of separation of variables.Separate the variables $y$ and $x$:$dy = \frac{1}{x} dx$.Now,integrate both sides:$\int dy = \int \frac{1}{x} dx$.The integral of $1$ with respect to $y$ is $y$,and the integral of $\frac{1}{x}$ with respect to $x$ is $\log|x|$.Adding the constant of integration $c$,we get:$y = \log|x| + c$.Thus,the correct option is $B$.

The solution of $\frac{dy}{dx} = \frac{1}{x}$ is

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