Solve the diffusion problem u(x,0) = {_-^2 otherwise {4 Ut - 3uxx = 0, -∞0 0 4 |x|>2 Write the solution in terms of the error

Q: Find all local maximum and minimum points of y = 2 + 3x − x³ by the second derivative test.

A: y = 2 + 3x - x3    => y' = dy/dx = 3 - 3x2 = 0 (set)                => 3(1 - x2) = 0…

Q: Solve the IVP, explicitly if possible. 3y x+9(-7)=1 (x– 7)* 8. y=(x+9)3 (x + 9|) yl = (x+9|)

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Q: -1² ƒ'(x) = 3x² √√x6 +1 If f(x) = √t² + 1 dt then

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Q: Find the best quadratic approximation, Q(x, y) of V9 + 7x + 5y for (x, y) near (0,0), Q(x, y) :…

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Q: Solve for a) given y= 2f(x) solve for x b) given y=-3f(2x) solve for x c) given y= f^-1 (4x) solve…

A: Given Functions are as follows

Q: f(t) = e^3t - cos(6t) - (e^3t)(cos(6t) * O F(s) = 1/(s-3) + s/(s*2 + 6*2) - (s-3)/(s*2 - 6x + 45) O…

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Q: X(s)=(s^2+6s+7)/(s^2+3s+2) and Re{s}>-1 what is x(t)?

A: We are given : X(s)=s2+6s+7s2+3s+2 ⇒X(s)=s2+3s+2+3s+5s2+3s+2 ⇒X(s)=1+3s+5s2+3s+2 ---(1) Now,…

Q: I want solve

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Q: y'-(2/x)y=(y^3)/(x^2) find the solution that satisfies y(1)=1

A: The given differential equation is

Q: -1 Find L s2–18s+40 s(s²–6s+10) |

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Q: Differentiate x4 - 4x + 3 - f(x) = Vx +1

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Q: 7 0-3 -9 -2 3 18 0-8 y, y(0) = 2 3

A: Given y'=70-3-9-23180-8y Also given y0=23-1   To reduce to row echelon form and solve for constant…

Q: Solve (1+x)x²y"-(1+2x)xy'+(1+2x)y=0

A: According to guidelines we can do only first question thank you.We have to solve differential…

Q: Find the particular solution for ysqrt(1-x^2) * y'-xsqrt(1-y^2)=0  when y(0)=1

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Q: Differentiate f (x) = 7 (2-60+3). A. f' (2) = a2-6x- 3 B. f' (x) = In(7)(2x–6)7™(=²-6z+3) x2-6x+3…

A: Differentiate f(x)

Q: y-y"+y'- y = xe* -e-x + 7

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Q: f(x)={ 5x2 ; x ≤ 0, 10x3 ; x > 0}  Compute f'(x)

A: Given: fx=5x2,x≤010x3,x>0

Q: Show that the f(x)=x-(In x)^{x} =0, has at least one solution in the interval [4, 5]. O f(4)=0.31,…

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Q: Solve the non-homogenous system Sa' = -x – y+ 3/2 ly = 2x – 4y Find lim-00 r(t)

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Q: 12 +9r V3x-5 If f'(x)= hat is one possible ((x);

A: answer is  f(x) = 8(3x-5)12 +3x3   detailed solution is given below

Q: (2/x+1)(x– 1) Find the f'(x) of the function f(x) = x+3

A: Given, f(x) = 2x+1x-1x+3 f(x) = 2x32-2x12+x-1x+3 We know that ddxxn = nxn-1  and quotient rule of…

Q: Help 18 cubic function whose graph has horizontal tangents at (-2,6) and (2₁0). {Y= ax ³ + bx²²…

A: Let's solve.

Q: Please use the conjugate gradient method to solve min구 + z. (): with the starting point r1)

A: We will convert the minimising function into matrix form to apply the conjugate gradient method.