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First Order Differential Equations

Differential Equations - dy/dx = g(y)

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

y=e^{3 x^3}+5

y=6 e^{3 x^3}

y=7 e^{3 x^3}

y=e^{3 x^3}+6

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by Brilliant Staff

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

y=4x^2+9

y^2=4x^2+9

y=8x^2+9

y^2=8x^2+9

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by Brilliant Staff

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

y=\frac{1}{\ln x-8}

y=\frac{1}{\ln x+8}

y=\frac{-1}{\ln x-8}

y=\frac{-1}{\ln x+8}

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by Brilliant Staff

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

e^{-y}=7-x

e^{-y}=x-7

y=-\ln \lvert{7-x}\rvert

y=\ln \lvert{7-x}\rvert

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by Brilliant Staff

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

y=-\frac{1}{4x^2+5}

y=-\frac{1}{4x^2-5}

y=\frac{1}{4x^2-5}

y=\frac{1}{4x^2+5}

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by Brilliant Staff

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