The integrating factor of the differential equation $x\large\frac{dy}{dx}$$-y=2x^2 is $(A)\;e^{-x}\qquad(B)\;e^{-y}\qquad(C)\;\frac{1}{x}\qquad(D)\;x$ 1 Answer Comment A) Need homework help? Click here. Toolbox: • If the equation is of the form \large\frac{dy}{dx}$$ + py= Q$, then the integrating factor is $e^{\large\int pdx}$
The equation can be rewritten as $\large\frac{dy}{dx }-\frac{ y}{x} =$$2x^2$
Here $p = \large\frac{-1}{x}$ and $Q = 2x^2$
Hence the integral Factor is $e^{\int (\large\frac{-1}{x})}dx = e^{\large-\log x} = e^{\large \log(1/x)} = 1/x$