I have absolutely no idea how to solve these:

SHOW THAT

1. $\displaystyle y=1/x$ (x doesNOT equal 0) satisfies the equation $\displaystyle x^3y^(2derivative) + x^2y^(1st derivative)- xy=0$

2.y=xe^-x satisfies xy^(1st derivative)= (1-x)y

3. y=xe^-x^2/2 satisfies xy^(1st derivative)= (1-x^2)y