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 Using the stated initial value problem. ' (0) 1 y xyy =+= (a) y0(x)=e x (b) y0(x)=1+x (c) y0(x)=cos(x) I only need y1, y2 and y3 from the above.

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 – a)x^(a+b+c-3). Are these functions linearly independent?

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 after the dose. Plot the function m(t) as it varies with time. After how many hours will the drug reach 10% of its initial value? After how many hours will it reach 1% of its initial value? 2. Now imagine that a drug (such as aspirin or an antibiotic) with a half-life of 12 hours is taken regularly every eight hours. Assume that the first dose is taken at time... click for more

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)=0. In this problem, since we will investigate free fall and terminal velocity, let's choose the positive direction for velocity and position as downward in the same direction as g; therefore, the coefficient of mg in the ODE is +1, not -1. 1. If there are no external forces acting on the object, then its velocity increases without bound (until the eobject collides ... click for more