Differential Equation dy/dx = 4sin(2x)/y

Find the general solution to the following differential equations:
(put in y= form, solve for c)

dy/dx = [4sin(2x)]/y

please show steps, thanks!

Separate the variables

dy/dx = 4 * sin(2x) / y
y * dy = 4 * sin(2x) * dx

Integrate

(1/2) * y^2 = 4 * (1/2) * (-1) * cos(2x) + C
y^2 = -4 * cos(2x) + C
y^2 = C - 4 * cos(2x)
y = +/- sqrt(C - 4 * cos(2x))

There is no need for brackets around a single term as you have here.

Find the general solution by separating the variables then integrating:
dy / dx = 4sin(2x) / y
y dy = 4sin(2x) dx
∫ y dy = ∫ 4sin(2x) dx
y² / 2 = -2cos(2x) + C
y² / 2 = C - 2cos(2x)
y² = C - 4cos(2x)
y = ±√[C - 4cos(2x)]

dy/dx = ( 4sin(2x) ) / y
y dy = 4sin(2x) dx
Integrate.
½y² = -2cos(2x) + constant
y² = -4cos(2x) + constant
y = ±√(c - 4cos(2x))