Find the function M that satisfies the following conditions: dM/dt= 8t^2−4 / t^2 ;M(4)=2. M(t)=?

Question

Find the function M that satisfies the following conditions:

dM/dt= 8t^2−4 / t^2 ;M(4)=2.

M(t)=?

Answer 1

M(t) = ∫(8t² - 4t^-2)dt = 8t³/3 + 4/t + C; M(4) = 8·4³/3 + 4/4 + C = 2; C = - 509/3.

M(t) = 8t³/3 + 4/t - 509/3