Question

Solve the differential equation. f '(x) = 4x, f(0) = 5 f(x) =

Answer 1

Answer: f(x) = 2x^2 + 5

Explanation:

First, integrate f'(x). Add +1 to the power and divide the function by that power. So, since the power of 4x is 1, the power would now be 2, 4x^2. Then, divide 4x^2 by 2 since the power is 2. 2x^2.

Now, we have f(x) = 2x^2 + c.

We know that f(0) = 5. We can find c with that information.

5 = 2(0)^2 + c

c = 5

f(x) = 2x^2 + 5.