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## First Order Differential Equations

These are equations, Calculus-style. From modeling real-world phenomenon, from the path of a rocket to the cooling of a physical object, Differential Equations are all around us.

# dy/dx = g(y)

If $$\displaystyle \frac{dy}{dx}=9x^2y$$ and $$y(0)=6,$$ which of the following is true?

If $$\displaystyle \frac{dy}{dx}=\frac{8x}{y}$$ and $$y(0)=3,$$ which of the following is true?

If $$\displaystyle \frac{dy}{dx}=\frac{y^2}{x}$$ and $$\displaystyle y(1)=\frac{1}{8},$$ which of the following is true?

If $$\displaystyle \frac{dy}{dx}=e^y$$ and $$y=0$$ when $$x=6,$$ which of the following is true?

If $$\displaystyle \frac{dy}{dx}=8xy^2$$ and $$\displaystyle y(0)=\frac{1}{5},$$ which of the following is true?

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