Exact Equations & Substitutions · Challenge problem

The equation $(3y + 4xy^2)\,dx + (2x + 3x^2y)\,dy = 0$ has an integrating factor of the form $\mu = x^ay^b$. Use it to solve the equation with $y(1) = 1$ (for $x, y > 0$), and find $y\!\left(\dfrac{16}{3}\right)$.