Answer
$2{y^4} = 5{x^2} + C$
Work Step by Step
$$\eqalign{
& \frac{{dy}}{{dx}} = \frac{x}{{{y^4}}} \cr
& {\text{Separating the variables}} \cr
& {y^4}dy = xdx \cr
& {\text{Integrate both sides of the equation}} \cr
& \int {{y^4}dy} = \int x dx \cr
& \frac{{{y^5}}}{5} = \frac{{{x^2}}}{2} + k \cr
& {\text{Multiply both sides by 10}} \cr
& 2{y^4} = 5{x^2} + 10k \cr
& {\text{Let 10}}k = C \cr
& 2{y^4} = 5{x^2} + C \cr} $$
