can you please help me solve this problem if dy/dx=ycosx and y=3 when x=0, then y=

Answer 1

dy/dx = y cos(x)
dy/y = cos(x) dx
ln y + const = sin(x) + const
ln y = sin(x) + const

ln 3 = sin(0) + const
const = ln 3

ln y = sin(x) + ln 3
ln y - ln 3 = sin(x)
ln (y/3) = sin(x)
y/3 = e^sin(x)
y = 3e^sin(x)