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.

Picard's Method of Successive Approximations

Please see the attached file for the fully formatted problems. Attached is a file with a three part successive approximation problem. The following problems are to use the method of successive approximations (Picard’s) [EQUATION] y x y fty tdt =+∫n− with a choice of initial approximation other than y0(x)=y0 ...continues

Using Wronskian to prove whether the functions are Linearly Independent or Linearly Dependent.

Wronskian of Functions Differential Equation Wronskian of Functions Define the Wronskian of functions. Show that the Wronskian of the functions x^a, x^b, x^c (x > 0) is equal to (a – b)(b – c)(c – ...continues

Orthogonal trajectories, family of curves 2cy+x^2=c^2, c>0

Please see attachment. Please help me solve problem in its entirety. I'm having trouble, most of all, solving the D.E. Thanks. :)

Differential Equation

Most drugs are eliminated from the body according to a strict exponential decay law. Here are two problems that illustrate the process. 1. The drug Valium has a half-life in the blood of 36 hours. Assume that a 50-milligram dose of Valium is taken at time t=0. Let m(t) be the amount of drug in the blood in milligrams t hours ...continues

Free Fall and Terminal Velocity

An object in free fall in a gravitational field is governed by the ODE m*dv/dt=mg + Fs, where m is the mass of the object, g=9.8 meters/sec is the acceleration of gravity, v(t) is the velocity of the object t seconds after it is realeased, and Fs denotes external forces acting on the object. In all that follows, assume that v(0 ...continues