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

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Answer 1 · 2016-11-01T20:00:53

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

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

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:
$g(x) = 2x^3 -1$

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