Please derive the following equations for the following two utility functions (using the parametersa,b,c, anddprovided above): U(x,y)=x³y²and U(x,y)=5lnx+5y. For the latter function, you can neglect the possible extreme case of having a corner solution, and focus only the interior solutions.

• Marshallian demand functions x(P_x,P_y,I) and y(P_x,P_y,I)
• Indirect utility function v(P_x,P_y,I)
• Hicksian demand functionsx^H(P_x,P_y, U) and y^H(P_x,P_y, U)
• Expenditure function E(P_x,P_y, U)