Consider the temperature in a uniform rod of length 2 if the initial temperature is f (x) = x %3D and if the end x = 0 is insulated while the other end is maintained zero degree tem- perature. (a) Find an initial-boundary value problem of PDE to model the temperature function u (x, t): (b) Solve this PDE.

Q: Consider dy = 4-t-2y dt y(0) = 1 Using At 0.1 find y(0.1), y(0.2), … ,y(1) using Runge Kutta Method.…

A: Given first order differential equation is dydt=4-t-2y, y(0)=1 So f(t,y)=4-t-2y, y(0)=1 Step size…

Q: A tank contains 50 kg of salt and 1000 L of water. Pure water enters a tank at the rate 10 L/min.…

A:

Q: Find C1, C2, and Ca so that the given functions will satisfy the prescribed initial conditions. 4a.…

A: We will find out the required values.

Q: where and dt=2' y(0) = 1, y(0.1) = 1.01, y(0.2) = 1.022 (03)

A:

Q: A large tank contains 20 liters of pure water. Then a process begins where water containing 50 grams…

A: We have to set up the equation

Q: A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire system is then…

A:

Q: The function u(x, t) = exp(-x²) is a solution of the heat equation 4rt au au² 30-3422 at ax² Use…

A: Given the solution ux,t=14πtexp-x24t of the heat equation ∂u∂t=∂2u∂x2.

Q: Use Secant method to to approximate the solution of f(r) = z+ cos z =0 accurate to within 10-3,…

A: The secant method is used to calculate the root of the function. The formula for the secant method…

Q: d²y =t+ cost di2 Q.4(20 Points): Find a function f(t) such that and such that y(0)%=D1 and y (0)=2.

A:

Q: Use the Runge-Kutta method to approximate x(0.2) and y(0.2). First use h = 0.2 and then useh = 0.1.…

A:

Q: Find a function y=P(t)that is a solution of y'=.02y with initial condition y=100 when t=0.

A:

Q: Let y be the solution of the initial value problem y" + y = – sin(2x), y (0) = 0, y' (0) = 0. The…

A:

Q: (Population Logistic Model) Let P(t) represent the population of a certain species at time t. The…

A: The main objective is to solve the population logistic model.   As per our guidelines I, allowed to…

Q: Solve the IVP Cost y +7Y y(T) = 0, t> 0 %3D t2

A: Given IVP is,  y'+2ty=costt2, yπ=0, t>0.   It is of the form of y'+Pty=Qt. Here, Pt=2t and…

Q: 6. An object is dropped from the top of a building 200 m high. The object encounters air resistance…

A: Solution :-

Q: 2. A 0.2kg weight stretches a spring 0.1m. The system is submerged in oil with damping coefficient…

A: Given the mass of the weight is 0.2 kg and the weight stretches the spring 0.1 m. The system is…

Q: The motion of a mass-spring system with damping is governed by y''(t) + by' (t) + 36y(t) = 0; y(0) =…

A: y''t+by't+36yt=0y0=3y'0=0b=10

Q: Solve the following Initial Value Problem: y' sinx = y(y − 1), y = y(x),y (7) = 2.

A: Here we have to solve the given initial value problem.

Q: 2. Analyse the following equations graphically: x = ex COS X (i) x = 1 - cos 2x (ii) Find all the…

A: 2. Given equations are: (i) x.=ex-cosx (ii) x.=1-cos2x   To Find: All equilibrium points, and…

Q: dY/dt =  ( 2  2 )Y.             with initial condition Yo=(1,1)              ( -4  6 ) a) find…

A: Given dydt=22-46y  with initial condition y0=1,1

Q: 5. Suppose heat is lost from the lateral surface of a thin rod of length L into a surrounding medium…

A: Given the heat equation is k∂2u∂x2-hu=∂u∂t, 0<x<L, t>0 The initial temperature is f(x)…

Q: A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then…

A: We have to find the equation of motion for given condition.

Q: Use Euler's method with specified step size to determine the solution to the given IVP at the…

A:

Q: Problem 8 Find the solution of the given initial value problem. Sketch the graph of the solution and…

A: Consider the given equation. y''+4y'+3y=0 Write the characteristic equation.…

Q: sove Solve the following initial value y' + 3y=e, y (0) = 7

A: Please see the below picture for detailed solution.

Q: Determine the longest interval in which the given initial value problem is certain to have a unique…

A:

Q: 4. Solve the IVP y' = 2x-3y +e¯* y'= 2x- 3 y +e * with y(0) = 1 y(0)= 1

A:

Q: b) Find the temperature u(x,t) from the heat equation in a laterally insulated copper bar 80 cm long…

A: Given:-            To find the temperature u (x, t)  from the heat equation in a laterally insulated…

Q: A 50 gallon tank initially contains 20 gallons of pure water. Salt solution, at 0.5 lb/gal, begins…

A:

Q: A horizontal beam of unit length under load w(x) satisfies the system: y" = M, M" = w(x), x = (0,…

A: