Question

How do you solve the differential equation given f'(x)=4x, f(0)=6?

Answer 1

Answer:

y = 4x²/2 + 6

Step-by-step explanation:

f'(x) = dy/dx

dy/dx = 4x

dy = 4x dx

∫dy = ∫4x dx

y = 4x²/2 + C

when x = 0 ; y = 6 [given]

C = y - 4x²/2

Substituting we get

6 - 0 = 6 = C

Hence equation is

y = 4x²/2 + 6