Question

How do you solve the differential equation given `g'(x)=6x^2`, g(0)=-1?

Answer 1

`g(x) = 2x^3 -1`

Explanation:

`g'(x) = 6x^2`

So we can integrate to get;

`g(x) = int 6x^2 dx`
`:. g(x) = 2x^3 + C`

Using the initial condition `g(0)=-1=>-1=0+C`
`:. C=-1`

Hence, the solution is:
`g(x) = 2x^3 -1`