1. ## Derivative HELP

I have absolutely no idea how to solve these:

SHOW THAT

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

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

2. You should calculate the derivatives and then plug them into the given equations to see if they are satisfied. For y=1/x, you have

y'=-1/x^2
y''=2/x^3.

Just substitute these into the equation. It works.