Solve using integrating factor (x^5+3y) dx-xdy=0

tnx

(x^5 + 3y) dx - xdy = 0

x^5 + 3y - xdy/dx = 0

3y - xdy/dx = - x^5

dy/dx - 3/x y = x^4

I. F. = e^∫ (-3/x) = 1/x^3

(dy/dx) / x^3 - (3/x) y/x^3 = x^4/x^3

(dy/dx) / x^3 - 3/x^4 y = x

(1/x^3 y) ' = x

∫ (1/x^3 y) 'dx = xdx

1/x^3 y = 1/2 x^2 + c

y = (x^5) / 2 + cx^3