y' =(ln x)/xy

y(1)=2

and

y'=y

y(0) = 1

HELP!

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- Mar 28th 2010, 03:53 PMpuravida12Solving differential equations..help!
y' =(ln x)/xy

y(1)=2

and

y'=y

y(0) = 1

HELP! - Mar 28th 2010, 04:02 PMpickslides

$\displaystyle \frac{dy}{dx} = \frac{\ln x}{xy}$

$\displaystyle y~dy = \frac{\ln x}{x}~dx$

$\displaystyle \int y~dy = \int \frac{\ln x}{x}~dx$

$\displaystyle \frac{dy}{dx} = y$

$\displaystyle \frac{dy}{y} = dx$

$\displaystyle \int \frac{dy}{y} = \int ~1 dx$