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# Separable Differential Equation $\frac{dy}{dx}=\frac{10}{y}$

SVCALC-WSXC5W

Solve the following differential equation where $y(0)=1$ and then determine the interval of validity for the solution.

$$\frac{dy}{dx}=\frac{10}{y}$$

A

$\sqrt{20x+1}$, $x\geq -\dfrac{1}{20}$

B

$20x+1$, $x$ all real numbers

C

$\sqrt{20x+2C}$, $x\geq -\dfrac{C}{10}$

D

$(20x+1)^{1/2}$, $x\geq -\dfrac{C}{20}$