Find the solutions for the problems by using the Euler-Lagrange differential equation and the boundary conditions, if given. I=(y2+4xy)dx=extremum.I=(y2+yy+y2)dr=extremumI=(xy2yy+y)dr=extremum I=042(y2+2yy16y2)dx=extremum. Bomdary conditions: y(0)=0,y(/8)=1. Find the solutions for the problems by using the Euler-Lagrange differential equation and the boundary conditions and constraints, if given. I=01v1+y2dx=extremun. Bomdary conditions: y(1))=0,(x,y))(x9)2+y2=9. I=0(y2y2)dx=extrennum. Construint: 0ydx=1 Find the Euler-Lagrange differential equation for the functionals. I=(x2(xu)2+y2(yu)2)dxdy=extremumI=ab(xy2+x2y+xy)dt=extremum