Write a in the form a = a-T+anN at the given value of t without finding T and N. %3D r(t) = (- 2t + 2)i + (3t)j + ( -t )k, t=3 OT+ ON a = (Type exact answers, using radicals as needed.)

Q: Let L(y)=(x-1)y" - xy + y a) with the observation that y, zx is a solution of L(4)=0 on (1,00), by…

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Q: H.W. Solve the fallowing first order DE.

A: Introduction: Integration will be used in some steps to solve a differential equation, both general…

Q: Let L(y)=(x-1)y" - xy + y a) with the observation that y, zx is a solution of L(4)=0 on (1,00), by…

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Q: d a value of r> 0 such that h(z) = z² +22³ + z + 1 has all its zeroes in D,(0).

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Q: ) Compute the four 4th roots of −T + Ti where T=7

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Q: A. Find the general solution of the following DE using the methods introduced in this unit unless…

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Q: Find the root of f Ca) = as +bx°+ dsinx between Xe2 and x =4 with the use of 4- Bise ction method a=…

A: Suppose the root of the function fx lies in the interval xn-1,xn. Use the following formulae, to…

Q: .(1) t is straightforward to show that y = k-1 is a solution to the homog quation

A: Given,                yk+2 -2k+1kyk+1+ kk-1yk=0         (3.151)and       yk+2 -2k+1kyk+1+…

Q: ker(A) = R104 %3D O ker(A) = {0} %3D ker(A) cannot be determined from this information

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Q: O Use the bisection method to numerically solve the nonlinear equation .1.5 f (x) = 40x3 –875x+35000…

A: Rffthh

Q: 5. EB = 33, BD = 5x - 10 and ED = 9x + 3. Find x. %3D O 2.9 5.8 OOO

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Q: The function def ined by y=Acos(In(x)) +Bsin(In(x)) d²y dy is the solution of the following DE: x²-…

A: True . i.e. the function defined by y=Acos(ln(x))+Bsin(ln(x)) is the solution of the differential…

Q: In 2r d.r. in terms of 2. (a) Define a substitution variable y and write J1 Do not solve the…

A: The objective is to find the value of the given integrals

Q: O Let n 3 be an integer. How many roots of the equation 2" + 3z +1 = 0 lie in the closed annulus {z…

A: We will use rouche's theorem.

Q: Using complexification, find the general solution of d²y dt2 dy +2- + 5y = 34 cos 2t. dt

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Q: In approximating the population in terms of t, P(t) = P(0) - tP'(0). If the current population of a…

A: This question is related to Functions, we will solve it using given information.

Q: Solve for for the equation y = aln(x + )+ 4tan(;)– 2x O a. T O b. In(4 + x) O c. none of these O d.…

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Q: 2) Use completing the square to find the following: s+4 а) L-1 ans: e-2t cos2t + e¬2tsin2t (s²+4S+8)…

A: We have to answer the following... a. L-1s+4s2+4s+8b. L-12ss2+12

Q: Find the general solution of a given non exact DE y(8x-9y)dx+2x(x-3y)dy=D0. (Note: Express your…

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Q: A quadratic equation x4-x-8=O is defined with an initial guess of 1 and 2. Find the approximated…

A: Given: The equation is x4-x-8=0 the initial guess x0=1 and x1=2 By the secant method, the iterative…

Q: (2) By using the secant method, find an iterative formula to find the value of ym where m is a…

A: Here x2-5=0∴x2-5=0Let f(x)=x2-5Here x 0 1 2 3 f(x) -5 -4 -1 4 1st iteration :x0=2 and…

Q: a.(2y²+2y+4x² ) dx + (2xytx )dy =D0

A: The solution is given as

Q: Work out the following | (2x + 1)e² -z da =

A: we use substitution method to solve this integration

Q: Solve h=ab+rh=ab+r for a

A: Given     h= ab + rh We can solve for a by separating it

Q: Solve e = 1 + V3i for all values of z

A: Given,              ez=1+3i

Q: Determine for which values of m the function (x)=x" is a solution to the given equation. dy (a) 2x2…

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Q: Evaluate V (6x + vy) ds where C is given in the accompanying figure. (1,1) 1- y=x y=x2 (0,0 ds =…

A: We need to evaluate integral.

Q: Solve a0 = 1, and an = 3an−1, for n ≥ 1 using the characteristic equation method.

A: We will start with the trial solution, an = rn to find the characteristic equation.

Q: solve the following P.D.E by separable method: a?u + 3у?и %3D 0 дхду

A: We solve the given partial differential equation by separable method. The given equation is…

Q: 5. Show that the equation (2y – 6æ) dx + (3x – 4x²y=') dy = 0 is not exact. Show that the polynomial…

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Q: Solve z+z +1= 0 by obtaining the roots. Answer a. b(1+jv3), }(-1± N) 幸 d. (1+ jv/3), (-1±jv3)

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Q: 4.)S V dx Use only The Method of substitution/u-substitution on this item. Final answer should be in…

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Q: 1) Rewrite c(r) = 2+5z+2 I-3 in the form y= q(x) + He where r has degree less than b.

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Use Euler method to approximate the value of y(0.2), given               ay' - by = ce^(kx) + mx  ,…

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Q: Find f, f, f. fx= f(x,y,z)=x-√√√²+z² (Type an exact answer, using radicals as needed.)

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Q: Find a general solution of each reducible second-order differ- ential equation x² y" + 3xy' = 2

A: Given: .....(1) Consider, Then,

Q: Find the eror in the work, then correct the mistake and find the correct answer Step Equation nol…

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Q: 5. Given the General Solution the DE, Identify the roots * y = C1e¬2x + C2cos2x + C3sin2x O A) m1=…

A: Here, the solution to the DE is: y=C1e-2x+C2cos 2x+C3sin 2x...(1)

Q: Solve e = 1+ V3i for all values of z

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Q: Evaluate: x 3* dx if a is equal to the first digit and bis equal to the second digit of the sum of…

A: Evaluate ∫abx3xdx

Q: Suppose * = f(). (a) Given y(xo) = Yo, when does this equation have a unique solution? = z(x, y) to…

A: Given- Suppose dydx = fymx To find-  Given yx0 = y0, when does this equation have a unique…

Q: (D++D²)y=3x²+4sin(x) – 2cos(x)

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Q: A stone, projected vertically upward with initial velocity 112 ft/sec, moves according to 8 = 112t -…

A: We have to choose correct option

Q: staté the form of the particular solution to y" – 6y +9y = kt + f(t)e³t +2 sin(1), where k is a…

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Q: f the auxiliary roots of a certain HLDE with constant coefficients are 2, -3, and -3, then the…

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Q: 3 (a) Given that T= 2n12g , express I in terms of T, g and n. %3D

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Q: Which is the solution to the equation 7n 37 2sin22x + 3sin2x + 1 = 0, x = 6

A: 2sin22x+3sin2x+1=0 Put x=7π6 in the given equation, we get…

Q: Solve for z in the equation 2-5j z+j+1 2= +3j 2z-j A) 0.2 + 0.1 j B) -0.2 + 0.1 j C) 0.2-0.1j D)…

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