Singular points and the method of Frobenius

In the following equations classify the point $x=0$ as ordinary, regular singular, or singular but not regular singular.

1. $y''+y=0$
2. $x^3y''+(1+x)y=0$
3. $xy''+x^5y'+y=0$
4. $\sin(x)y''-y=0$
5. $\cos(x)y''-\sin(x)y=0$

Find the general solution of $x^2 y'' -y = 0$.

Find a particular solution of $x^2 y'' +(x-\nicefrac{3}{4})y = 0$.

Find the general solution of $x^2 y'' - x y' +y = 0$.