The Heat Equation on [0, L] solve the problem ди a²u =k- + F(x, t) for 00, at əx² u(0, t) = u(L, t)=0 for t≥0, u(x, 0)= f(x) for 0 ≤x≤ L. k=1, F(x, t) = t cos(x), f(x) = x²(5-x), L=5

Q: Assume that all functions are continuous on some interval (a, b). Prove that if y₁ and y2 are…

A: Since we are given that y1 and y2 are solutions of the differential equations  y' + p(x)y = f1(x)…

Q: 0, x<0, F(x) = { 공x?, O<x<2, 1, x22 a) Find E[X]. b) Find P(X 21|X)

A: From the distribution function we get:f(x)=ddxF(x)=ddx14x2=x2 for 0≤x&lt;2f(x)=0 otherwise. So,…

Q: (b) y'+y=f(t), y(0) = 0, where f(t) = 0 for 0 ≤ t < 1 and f(t) = 5 for t ≥1.

A: The given differential equation is , .Where .We know that a differentiable function is continuous as…

Q: Let f(x, y) = x2 – y?. Find (a) The directional derivative of f at (-2, 1) in the direction of v = i…

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Q: Let u = u(x, t), x, t ≤ R. Solve Ut + 5ux + u = 0 u(x, 1) = = COS X

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Q: The slope field for y' = x - xy is given below. Sketch the solution that satisfies the condition…

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Q: For positive constants A and B, the force between two atoms in a molecule is given f(r) = 1 + 2/3,…

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Let f(x, y) = + tan(xy – x³) , find дудх x-4y5 O a. 80y4 + sec2(xy – x³)(1+ (xy – 3x³) tan(xy – x³))…

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Q: Find the partial derivative Əz Əx for the function z = 8y²√x.

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Q: 3. Given f(x,y)=sin²(2x+3y²)-e+*y: (a) Find f,(x,y). (b) Find f,(x,y).

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Q: Utt || for 0 < x < T u(x, 0) = x? u:(x, 0) = }cos(8x) Uz(0, t) = u„(r, t) = 0

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Q: pont Let f(x) = 2x' + 1. a) Find f(x + h): -1 b) Find f(x + h)– f(x): c) Find (x+h)ー (x) d) Find…

A: a)   f(x)= 2x3+1f(x+h)= 2(x+h)3+1                         =2(x3+3x2h+3xh2+h3)+1…