Solve the differential equation $y^{\text{'}\text{'}}{x}^{2}y=0$ by using a power series centered at $x=0.$

Use a power series centered at $x=0$ to find the first four non$-$zero terms of the solution to $y^{\text{'}\text{'}}-2x{y}^{\text{'}}2y=0.$

Solve the equation $y^{\text{'}\text{'}}4y=0$ using a power series about $x=0$ and write the recurrence relation.

Classify $x=0$ as an ordinary point, regular singular point, or irregular singular point for the equation $x^2{y}^{\text{'}\text{'}}3x{y}^{\text{'}}y=0.$

Determine the type of the point $x=0$ for the differential equation $-1.$