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