Solving First Order Separable Ordinary Differential Equation With Initial Value

Solve the initial value problem dy/dx=(3x^2+4x+2)/[2(y-1)], y(0)=-1

Cauchy-Euler or Equidemensional Equations.

I'm taking differential equations I and we are studying non homogeneous equations. There is a problem concerning Cauchy-Euler equations that I don't understand. I need help with the solution. I have attached a word document with the problem.

Radius of Convergence

The problem is to determine the radius of convergence of the Taylor Series for each of the functions below centered at x. We are to explain our conclusion in each case. I would like to see how to work each problem (including what the Taylor Series is) and what the explanation is.

Bessel and Legendre's Equations - Finding Lower Bound

The problem is to determine a lower bound for the radius of convergence for the two following equations. I am able to get p(x) and q(x) for both equations, but I'm confused on how to proceed. I would like to see the problem worked out and what the lower bound is.

Solutions to Airy's Equation

I am having trouble getting the general solution for Airy's Equation. My work is attached in jpeg format. Also attached are the questions. I am looking to see if my work so far is correct in each question, and then how to get the general solution in question 4.