# Thread: equation of a curve

1. ## equation of a curve

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

2. 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.