$2-$ A two$-$dimensional strain field is given by:

$x=c(-x^2+\frac{7}{3}{y}^2),y=c(\frac{1}{3}{x}^3-\frac{5}{3}{y}^2),xy=\frac{1}{3}bxy($b and c are nonzero constants$)$

a$)$ What is the relationship between $b$ and $c$ if this field satisfies the strain compatibility conditions?

b$)$ Determine the displacements $u$ and $v$ corresponding to this field of strain at point $(5,2)$ if they are zero at point $(0,0).$ Use as a value of $4$ for $c.$