The first one I am not sure at all about but is the second one homogenous with a substitution required of ?
For the first one I guess that there is a typo . Second one is non-exact differential equation so you should apply Integrating Factor Technique :
Let's denote :
$\displaystyle M=-(x^4+y^4) ~\text{and}~N=xy^3 $
$\displaystyle \frac{\partial M}{\partial y}=-4y^3 ~ \text{and}~\frac{\partial N}{\partial x}=y^3 $
Since :
$\displaystyle \frac{\frac{\partial M}{\partial y}-\frac{\partial N}{\partial x}}{N}=\frac{-5y^3}{xy^3}=\frac{-5}{x} $
Integrating actor is :
$\displaystyle u(x)=e^{-\int \frac{5}{x} \,dx} $