find K(K)using two Puvtor roadby Bytlal of vaction adcontour integra tiban methods when £ K(Z) 2?-32+2 The outPut solutiou ust be K(K)=[{-13 uCk)

Q: y' = /2y – 1, у(1) — 1.

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Q: Q6) A string of infinite length is stretched from -0o to +00 and subjected to the following initial…

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Q: For the function f(x, y) = −xy2, find the solution from x = 0 to x = 1 with an increment of 0.2 by…

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Q: Use a third order polynomial approximation of s(t) to approximate the velocity at t=30s using a.…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3) Find the general solution by using reduction of order method to ty" – (t + 1)y' + y = 0 given…

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Q: Q2: Consider the IVP: y=1+,1srs2, y(1)=2. 1. Use 2d order Taylor's method to approximate the…

A: Consider the given IVP as follow : y/=1+yt, 1≤t≤2 , y(1)=2 i.e  x0=1,y0=2 and given that step-size ,…

Q: Find the general solution by using reduction of order method to ty" – (t + 1)y' + y = 0 given that…

A:

Q: Q2: Consider the IVP: y' =1+2,1sıs2, y(1) = 2. 1. Use 2d order Taylor's method to approximate the…

A: Given equation is  y'=1+yt                        (i) With initial condition y1=2 Here,…

Q: Consider the IVP r"(t) + = e-az(), r(0) = ro, r (0) = 0, where ro > 0, a > 0. (a) Solve the above…

A: We are given a second order non-homogeneous nonlinear differential equation as an IVP. And to prove…

Q: Determine y at t=0.2 (0.2) 0.8 by the fourth order Runge-Kutta method, given that y'=ity' y(0)=2

A: It is provided that y'=1t+y, y(0)=2. We need to determine y at t=0.2 0.2 0.8 by RK-4 method.

Q: Q2: Use Bisection method to solve -0.146843% f(x) = 668.06 (1 - e )- 40 with Xu =16 %3D and x2 = 12]…

A: The objective is to solve the equation fx=668.06x1-e-0.146843x-40 By Bisection method with xu=16 and…

Q: The orthogonal trajectories of r = 5a sin 0 is, where a is an arbitrary constant r = csin 0 O r5 = c…

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Q: Use a third order polynomial approximation of s(t) to approximate the velocity at t=30s using Direct…

A: Note:- As per our guidelines, we can answer the first part only because both the sub parts have…

Q: Given that y' = 2x2 – y + 3y2, where y = 0.5 at x = 2. Estimate the values of y(2.4) using the…

A: Let y'=f(x, y). Runge-kutta method of  fourth order also known as RK-4 method uses the formulas…

Q: Q1: Solve the following boundary value problems using the finite difference method and central…

A: Given that y''-3y'+2y=0, y1=2, y2=0, h=14

Q: For this initial value problem, compute the first two approximations U, and u, given by Euler's…

A: By uaing eular method

Q: Consider the IVP: x" + 4tx = 0, x(0) : - 1, x'(0) - 3 Using the Euler method with a time step of At…

A: Given, x''+4tx=0, x0=-1, x'0=-3, ∆t=0.5 Now, by Euler's method xn+1=xn+hpn=xn+∆tpnAnd,…

Q: Use Euler method to approximate the value of y(0.1), given               y' - 4y = 3x2 ,  y(0) = 4…

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Q: Consider xy' = y(lnx - Iny) with y(1) = 4. Using Runge-Kutta method with h=0.1, approximate y…

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Q: Use Runge-Kutta method of order four with step-size h = 0.5 to approximate the solution for 2<t<3 of…

A: given IVP isdydt=-y+ty1/2y(2)=2h=0.5here dydt=f(t,y)where f(t,y)=-y+ty1/2t0=2y0=2h=0.5by using R.K…

Q: The initial temperature of a long thin rod is u(x, 0) = 40, and the rod is divided into three equal…

A: Given the initial temperature function is, ux,0=40 As we know, ∂T∂t=α∂2T∂x2 Where,  α=0.8…

Q: Find the point that mdximizes the f(xg)= x?+y?- 6x +9 funciion depercling on the g(x,y)=y-x²=0…

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Q: Solve the ODE over the interval from t=0 to 0.4 using a step size of 0.1. The initial conditions are…

A: ODE over the interval from t =0 to t =.4 using a step size of .1. We have to find by two methods…

Q: Q3: Fill in the blanks 1- In _methods proper choice of initial value is very important. rule is used…

A: "Since you have posted a question with multisubparts, we will solve first three parts for you. To…

Q: azz 2. A. If z = sin(3x+2y) , verify that 2 - 3 a2z = -6z ay2 B. If f = x³y³ + 2xcosy + y² lnx then…

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Q: Using the Method of Undetermined Coefficients, a suitabie choice for the nonhomogeneous solution yw…

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Q: Q5) Evaluate the integral 0.61-10 (6.73x + 4.3025 - 10- dx 2.316 • 10-11 122-10- Using trapezoidal…

A: The solution to the integral can be calculated using numerical methods. The formula for the…

Q: 2. The concentration of a pollutant bacteria c in a lake decreases rapidly according to c(t) =…

A:

Q: 5 By separation of variables, Solve the followin PDES :- du dt d2u dx2 @ o U (0₂t) =(4,t) = G u(x,0)…

A: Given is the Partial Differential equation ∂u∂t=2∂2u∂x2…

Q: Solve using the bisection method f(x) = e-x* – 2x + 1 starting at the interval [0.75,1]

A: Consider the provided question, We have to solve the given function by using the bisection method,

Q: 5) Find the general solution by using reduction of order method to t'y" – ty' – 3y = 0 given that y,…

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Q: The wall (thickness L) of a furnace is comprised of brick material (thermal conductivity, k = 0.2…

A: Given heat equation is ρc∂u∂t=k∂2u∂x2                    (1) initial condition is u(x,0)=x2(L-x)…

Q: x' + 2e* – In xr- 3 = 0

A:

Q: Q2: Consider the IVP: y=1+,1sıs2, y(1)=2. 1. Use 2d order Taylor's method to approximate the…

A: Step:-1 Taylor's Method of second order :- yxi+1=yxi +h y'xi +h22y''xi ----(1) Given that y'=1+yt,…

Q: find the suprimum, in! infimum maximum and minimum of { c,1": (1+):ne w}, if t)ine w}

A: Supremum: Let A⊂ℝ then, least upper bound of the set is called supremum  of the set A. Supremum may…

Q: Consider the following IVP: y' (t) =1+, y (1) =2, with n=5 1sts2, The actual solution of this IVP is…

A:

Q: Q6) A string of infinite length is stretched from -0 to +0 and subjected to the following initial…

A: Given vx=1-1≤x&lt;0-10≤x≤10otherwise

Q: z+1 Calculate using residue integration method f. ;dz, c: |z – 1| = 1. z4-2z3

A: Given, ∮Cz+1z4-2z3dz,C:z-1=1 Here given the circle with radius 1 and center (1, 0).

Q: Q5) Evaluate the integral 0.61-10 (6.73x + 4.3025 107 dx 2.316 10-11 1.22-10 Using trapezoidal and…

A: The integration can be calculated using the numerical method. The formula for the trapezoidal rule…

Q: S y' = % + 1, 1<t< 2 y (1) = 2

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Q: The orthogonal trajectories of r = 5a sin 0 is , where a is an arbitrary constant p = c cos 0 r=…

A:

Q: Consider the 1* order initial value problerm: y' = f(t, y), 1St<4, y(1) = yo A certain method is…

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Q: Consider xy' = y(lnx - In y) with y(1) = 4. Using Runge-Kutta method with h-0.1, approximate y…

A: Given,xy'=y(lnx-lny) y(1)=4; h=0.1To find: y'(1.3) using Runge-Kutta method

Q: Estimate x using the trapezoid rule withn=4 a. Type equation here. Redo 9 using Simpson's rule. a.…

A: Given  f(x) = x3  a = 0 , b = 4 , n = 4

Q: Use Runge-Kutta method of order four with step-size h = 0.25 to approximate the solution for 2 st<3…

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Q: Q6) A string of infinite length is stretched from -00 to +o0 and subjected to the following initial…

A:

Q: Use the Euler method to find an approximation for r(0.3) if r(t) is the solution of the initial…

A:

Q: Q6) A string of infinite length is stretched from -00 to +0 and subjected to the following initial…

A: Given vx=1-1≤x&lt;0-10≤x≤10otherwise