Question

find the particular antiderivative of the following derivative that satisfies the given condition dy/dx=4x^-4+9x^-1-1; y(1)=2

Answer 1

\[\frac{dy}{dx}=\frac{4}{x^4}+\frac{9}{x}-1\\
y=-\frac{4}{3x^3}+9\ln|x|-x+C\]
Plug in the given condition:
\[2=-\frac{4}{3}-1+C~~\Rightarrow~~C=\frac{13}{3}\]