Mathematics: Solve the differential equation

Solve the differential equation - id13450222, jaden120

CameronVand21

23.06.2021

f(x) = 3x^2+8

Step-by-step explanation:

We are given the first derivative of f(x) and the value of f(0) .

To go from the first derivative to the original function, we integrate.

Therefore:

$f(x) = \int {6x} \, dx$

To integrate, we add 1 to the power and divide by the new power:

$\int {6x} \, dx = \frac{6x^2}{2} =3x^2+C$

Because we have an indefinite integral, we have to add the constant, , to the end.

So: f(x) = 3x^2+C

We know f(0) so we can find the constant .

f(0)=3(0)^2+C=8

C=8

Therefore f(x) = 3x^2+8

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