each point (x,y) on a certain curve, the slope of the curve is 4xy. If the curve contains the point (0,4), then its equation is: A) y = e^(2x^2) + 4 B) y = e^(2x^2) + 3 C) y = 4e^(2x^2) D) y^2 = 2x^2 + 4 E) y = 2x^2 + 4
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Originally Posted by DINOCALC09 each point (x,y) on a certain curve, the slope of the curve is 4xy. If the curve contains the point (0,4), then its equation is: A) y = e^(2x^2) + 4 B) y = e^(2x^2) + 3 C) y = 4e^(2x^2) D) y^2 = 2x^2 + 4 E) y = 2x^2 + 4 You need to solve $\displaystyle \frac{dy}{dx} = 4xy \Rightarrow \frac{dy}{y} = 4x \, dx \Rightarrow \int \frac{dy}{y} = \int 4x \, dx ........ $ subject to the given condition y(0) = 4 ..... Note: Just on the basis of the given condition you can eliminate option A.
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