dydx=3x2−4\frac{dy}{dx} = 3x^{2} - 4dxdy=3x2−4
y=∫(3x2−4) dx=x3−4x+cy = \int (3x^{2} - 4) \, dx = x^{3} - 4x + cy=∫(3x2−4)dx=x3−4x+c
y = 6 when x = 3
6=33−4(3)+c ⟹ 6=27−12+c6 = 3^{3} - 4(3) + c \implies 6 = 27 - 12 + c6=33−4(3)+c⟹6=27−12+c
c=6−15=−9c = 6 - 15 = -9c=6−15=−9
y=x3−4x−9y = x^{3} - 4x - 9y=x3−4x−9
