$6.$ Solve initial value problem $\frac{dy}{dx}=y^2$

$y(1)=2$

$7.$ If $f(x,y)=x^3+x^2{y}^3-2y^2,$ find $f_x$ and $f_y.$

$8.{}_D(x+2y)dA,$ where $D=[1,2][0,1]$

$9.{\displaystyle \underset{0}{\overset{1}{}}}{\displaystyle \underset{3y}{\overset{3}{}}}{e}^{x^2}dxdy$

$10.$ If $f(x,y)=x^2+y^2-2x-6y+14,$ find the maximum and minimum value.