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# Separable Differential Equation with Fractions

SVCALC-BJ3IRN

Solve the following differential equation where $y(0)=10$ and determine the interval of validity for the solution.

$$\frac{dy}{dx}=\frac{1}{y}$$

A

$y(x)=\sqrt{2x +100},$ $x \mbox{ all real numbers}$

B

$y(x)=\sqrt{2x +100},$ $x \geq -50$

C

$y(x)=\sqrt{2x+50C},$ $x\geq -50$

D

$y(x)=\sqrt{x+50},$ $x \geq -50$