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

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.