Find the particular antiderivative that satisfies the following conditions

dy/dx=7x^[−2]+8x^[−1]−6;y(1)=2.

2 answers

dy/dx = 7/x^2 + 8/x - 6
y = -7/x + 8 lnx - 6x + C
using the point (1,2) we get
-7 + 0 - 6 + C = 2
C = 15
so,
y = -7/x + 8 lnx - 6x + 15
Thank you