I was solving a calculus of variational problem in two variables. After applying the conditions I get the following system of differential equations, $$18xy'(t)+2yy'(t)=0\\4yx'(t)+18xx'(t)=0$$ I am not familiar with these kind of system. I searched online, but I couldn't find any. Anyone can help?
Edit: Minimize the $$I(x, y)=\int_{t_0}^t9x^2y'(t)-2y^2x'(t)$$