Find the particular antiderivative that satisfies the following conditions: dy/dx=7(x^−2)+5(x^−1)−2; y(1)=4.

Answer 1

y = f(x) = -7 x^-1 -5 ln x - 2x + C

4 = f(1) = -7 - 5 - ln(1) - 2(1) + c

4 = -7 -2 + c

4 = -9 + c

c = 13

f(x) = -7 x^ (-1) - 5 ln x - 2x + 13