Find the particular solution of the differential equation that satisfies the initial condition(s). g'(x) = 4x2, g(−1) = 5

Answer 1

Hi Aaron,

To find the general solution, g(x), we need to integrate the function g'(x):

g(x) = integral (4x²) = (4/3)x³ + C (using the power rule)

Now, to find the particular solution, we know our function g(x) passes through the point (-1,5), so we should substitute this point into the function g(x) in order to solve for our arbitrary constant, C:

5 = (4/3)(-1)³ + C

5 = -(4/3) + C

5 + (4/3) = C

C = 19/3

Putting it all together, our particular solution is g(x) = (4/3)x³ + (19/3)

I hope this helps!