: Solve by using Separation of variables method? E= k a²u for 0 < x < L, t > 0 u(0,t) = u(L,t) = 0 for t > 0, u(x,0) = x(L-x) for 0< x < L

Q: 3y = /2y – 1, y(1) = 1. ) Find the solution y = y(x) of this IVP. Please present your solution y =…

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Q: how that x³ + 2x = -1 has a solution in an interval of length. You may find s helpful to complete…

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Q: The domain of the function g(x, y) = Select one: y-x x² +1 Dg = {(x, y)/(x, y) is above the first…

A: here we need to check where function become undefined and then solve for those conditions.

Q: Given the function, x = 3 + Vx? + y² , find y. Vx² +y² - X y Vx² + y? - > ア= y Vx? + y² + x ア= y Vx?…

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Q: TI. ExereISC Find the x-value of all points where the functions defined as follows have any relative…

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Q: Q1/ Solve the equation: 4fxx(x,t)=ft(x,t) f(x, 0)=20(6-x) f(0,t)=0 f(6,t)=0 Take h=1 for 0< t <2 and…

A: We suppose, ux,t=XxTt So, utx,t=XxT'tuxx,t=X'xTtuxxx,t=X''xTt So, from the given partial…

Q: f(x, y) = 2x -y-e-* = 0 g(x, y) = -x +2y-e-y = 0 a) For X₁ = 1 and fx(x₁, y₁) = fy(x₁, y₁) = 9x(x₁,…

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Q: The productivity of a certain country with the utilization of x units of labor and y units of…

A: Given, The productivity function f(x,y) = 100x0.72y0.28 Where  x is units of labor and y is units of…

Q: R = BYn+Ssyn B + 2yn (1+5²) 1/2 22.9Yn+4yn² 22.9+2yn (1+4211/2 12833 = (22.9 yn + 4yn²). 1.…

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Q: What is the general solution to 3yy' – x² = 0 for æ > 0? O y = a3 + C2 O y = '음교3 + C2 9. O y = /žæ³…

A: using variable separation method,

Q: f(x,t)=x²+14x+y²-4y+3. Pls find maxima, minima, & saddle points. Thank you & I will give thumbs up.

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Q: Determine the following value: F20 + F30 1. 2. F34 3. F67

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Q: ind and classify all critical points of the function f(x,y) = 3x²y + y³ – 3x² – 3y² + 2.

A: We have to find and classify the critical point of f(x,y).

Q: Find the least squares quadratic which best fits the curve Y= ex interval •< X<I ao+aix +azx over…

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Q: Find the functions x*(r) and y*(r) such that x = x*(r) and y = y*(r) solve the problem max f(x, y,…

A: max fx , y, r=max-x2-xy-2y2+2rx+2ry To Find: x*r , y*r such that x=x*r ,y= y*r.

Q: If G(2) = S. 4t° -2t J-4x TeA _t² +3 dt, then G(x ) = 0. ett True False

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Q: Solve the equation Ut u(0, t) u(4, t) u(x, 0) - = 2urr 3 -5 = 2

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Q: Find the extreme values of f ( x , y ) = x − 2 y subject to g ( x , y ) = x 2 + y 2 = 20. Both max…

A: Maxima or minima: If f(x) is any function then 1) Evaluate f'(x)=0 for critical point. 2) Evaluate…

Q: Find the extreme values ​​of f(x, y) = 2xy subject to the condition x + y = 2.

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Q: Find the co perpendicular to the li

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Q: ompany determines that monthly sales S(t), in thousands of dollars, after t months of marketing a…

A: Given:  s(t)=3t^3 - 50 t^2 +230t+180(a). Find; s'(t),s'(2),s'(3),s'(5)And…

Q: Use the method of separation of variables to solve: - = 0 in (0,1)×(0,+∞), at? ôx (1) u(0,t) = u(1,…

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Q: a) After using the ansatz u(x, t) = X(z)T(t), which equations do you get? Pick only two. (below C'…

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-parts…

Q: The height h (um) of a particle relative to a fixed reference point depends on the position of the x…

A: Please see the below picture for detailed solution.

Q: Use method of characteristics to solve ux+uuy=0 with u(0,y)=2y. What is the domain of validity? Is…

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Q: Solve Ut=a²uxx, 0<x<L, ur(0, t) = 0, ux (L, t) = 0, u(x,0) = f(x).

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Q: Use de Moivre’s theorem with n = 4 to prove that cos(4θ) = 8 cos^4 (θ) − 8 cos^2 (θ) + 1

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Q: Q1/ Solve the equation: 4fxx(x,t)= ft(x,t) f(x, 0)=10(6-x) f(0,t)=0 f(4,t)=0 Take h=1 for 0< t <2…

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Q: s) Consider the ODE y" - 4y + 4y = (2x² - x)e². Use the method of variation of parameter to compute…

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