Solve the initial value problem for the heat equation with time-dependent sources au = k+ Q(x, t) at ax u(x, 0) = f(x) subject to the following boundary conditions: Pls show the all steps, solve this thx (а) и(0, г) — А #0, u(L, t) = 0

Q: у" + 9у %3D 0, у (0) — 2, у'(0) 3D 0

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Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A: This is a problem of Differential Geometry.

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

A: b) Given :-  The temperature ux,t from the heat equation in a laterally insulated copper bar 80 cm…

Q: Solve the following partial differential equation: azy C2. ax? for 0 0 at2

A: In this question, we solve the wave equation δ2yδt2=c2δ2yδx2withy(0,t)=y(L,t)=0and y(x,0)=f(x)in…

Q: A 3 cm length silver bar with a constant cross section area 1 cm (density 10 g/cm, thermal…

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Q: Apply the initial conditions y(0) = 1, y'(0) = 4 to find c1 and c2 given that y = c1x + c2e2x

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Q: y" +y = 3 et/2) y(0) = 4 y(0) = 3

A: Second order non Homogeneous differential equation

Q: Solve the equation: b) y'= ex-y with an initial condition y(0)=1,

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Q: Use variation of parameters to find a general solution: y(3) – 4y = et.

A: Given differential equation: y3-4y'=et         ...(1)

Q: y" + 3y' + 2y = cos(e).

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Q: Solve y (t) + 5y (t) + 4y(t) = h(t); y(0) = 0, y (0) - 2 where h(t)%3D tfor0 s t S2 h(t) = (2t +…

A: A differential equation with the initial conditions is called an initial value problem. In this…

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: Find y(3) for y' = 1 + (x-y)2, y(2) = 1 by using Improved Euller's method. h = 0.5

A: Given  y'=1+x-y2 y2=1, h=0.5 We will find the value of y3

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: 4. y' +y = -x/y

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: The solution of the IVP y" – 3y' – 4y=0, y(0)=0, y'(0)=5 is: Select one: a. y= -e 4t+ e! b. y = -…

A: Using Method of Laplace Transform to solve IVP

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

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Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

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Q: 2²y" - 4.xy+6y= 0, y(2)=0, y'(2) = 4 %3D

A: The differential equation is given as x2y''-4xy'+6y=0x2D2y-4xDy+6y=0x2D2-4xD+6y=0 It is a Cauchy…

Q: homogeneous solution to the second order constant coefficient ODE’s. Solution must be real.

A: d3dx3y-3d2dx2y+3ddxy-y=0 A linear homogeneous ODE with constant coefficients has the form of…

Q: 2 A 3 cm length silver bar with a constant cross section area 1 cm² (density 10 g/cm³, thermal…

A: Let L, K, σ and ρ denote the length, thermal conductivity, specific heat and density, respectively.…

Q: Verify that the function u=e(-α^2)t sin x is a solution of the heat conduction equation ut = α2uxx

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Q: Find general solution of U" + U = 0.

A: Given differentiation equation is U''+U=0. We have to find the general solution of the given…

Q: Consider the initial value problem (IVP): x²y" + xy'-y= 0, y(1)=0, y'(1)=2. It can be shown that y₁…

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Q: [23] R and f 5 sec(t) 0

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Q: The following are three different methods for solving y (t) = f(t, y(t)): (A) Yn+1 = Yn + ¥ [S(tn,…

A: Given : three different methods for solving y't=ft,yt : A yn+1=yn+∆t2ftn,yn+ftn+∆t, yn+∆t ftn,ynB…

Q: y = C1cos(x) + C2sin(x) is a two-parameter of the: y" + y = 0. Look for a solution that is competes…

A: Here we put the initial conditions to find C1 and C2

Q: Solve the initial value problem: x²y"-2xy' +2y=0, y(1)=2, y'(1)=0.

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Q: Q2: (a): Solve (i) (x² D² – xD – 151I)y = 0 y(1) = 0.1, y'(1) = -4.5 (ii) 100 – 20 + d? N dN dt? dt

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Q: y? when y dy and x = 1. Find the particular solution to dz

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

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Q: y" – y' = sin(t) y(0) = 1 y' (0) = -1

A: We have to solve the IVP           y''-y'=sinty0=1y'0=-1

Q: Use the backward Euler method with h = 0.1 y'(t) + 1000cos(y(t))-100t = 0 y(0) = -0.5   find y(2)

A: Given y'(t) + 1000cos(y(t))-100t = 0 y(0) = -0.5and h = 0.1