DIFFERENTIATION RULES

The slope of the curve at any point P(x , y) is twice the y-coordinate of P.

i.e. dy/dx│P(x , y) = 2y

dy/dx = 2y

∫dy / (2y) = ∫dx

1/2 lny = x + C, where C is a constant

y = Ae2x, where A is a constant

Since the curve passes through (0 , 5)

So, 5 = A(1), A = 5

Hence, equation of the curve: y = 5e2x