Hi
Need help on the following question:
Find the general solution of the differential equation
$\displaystyle \frac{dy}{dx}-\frac{4y}{x}=e^{x^{-3}}$
$\displaystyle p(x)=\frac{-4}{x}$
$\displaystyle q(x)=e^{x^{-3}}$
$\displaystyle I=e^{\int \frac{-4}{x} dx$
$\displaystyle I=e^{ln|x^{-4}|}$
$\displaystyle I=x^{-4}$
$\displaystyle x^{-4}y=\int x^{-4}e^{x^{-3}} dx$
ok, i tried to integrate by parts however i never get the correct answer.
this is what i did
$\displaystyle u = e^{x^{-3}}$
$\displaystyle du = -3x^{x^{-3}}$
$\displaystyle dv = x^{-5}$
$\displaystyle v = \frac{x^{-4}}{-4}$
i have also tried the other way but still not correct.
P.S