Question

Solve the differential equation

Answer 1

Answer:

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

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, $c$, to the end.

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

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

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

$C=8$

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

Answer 2

F(x)=3x2+8 . Yw. Baiiii