Verified answer

dy/dx= 3y

dy/y= 3 dx

ln|y|= 3x + C

y= ce^(3x)

y(0)= 2, c=2

y= 2e^(3x)

:-

(1/3) $ dy/y = $ dx

(1/3) log y = x + C

(1/3) log 2 = C

(1/3) log y = x + (1/3) log 2

log y = 3x + log 2

y = e^(3x + log 2)

y = 2 e^(3x)