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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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