Find the particular antiderivative that satisfies the following conditions:

Question

dy/dx=7(x^−2)+5(x^−1)−2; y(1)=4.

Answer 1

y' = 7/x^2 + 5/x - 2
y = -7/x + 5lnx - 2x + C
so now you have
-7 + 0 - 2 + C = 4
C = 13

y = -7/x + 5lnx - 2x + 13

Answer 2

thank you!