Question $2$:

Determine the relations among the constants $a_0,a_1,b_0,b_1,c_0,c_1,$ and $c_2$

so that the following is a possible state of strain:

${}_x=a_0+a_1(x^2+y^2)+(x^4+y^4)$

${}_y=b_0+b_1(x^2+y^2)+(x^4+y^4)$

${}_{xy}=c_0+c_{1}xy(x^2+y^2+c_2)$

${}_z={}_{yz}={}_{xz}=0$