Solve the initial-boundary value problem for u(x, t): ди J²u Ət = 4- əx² u(0, t) = u(2, t) = 0 u(x, 0) = = fo, 0≤x≤1 5, 1 0 t> 0 dentify the type of the equation and the boundary conditions, clearly state the paramete 3) and reproduce the formula for the general solution you are using. Simplify your ans Hentities for sin(nn) and cos(nn) with integer n, but leave other terms intact. AS ဆုံကာ

Q: x3 dx (x – 1)5 y = Select one:

A: First evaluate the integral by substitute method. Then apply the limits of integral.

Q: Q1: Find the derivative of f(x,y,z)=x^2+xy^3-z at point P_o (1,1,0) in the direction of vector V…

A:

Q: Find the equilibria of x_(t+1)=0.9x_(t) when t= 0, 1, 2, 3 ... and use cobbwebing to determine the…

A: According to the given information, it is required to find equilibria.

Q: along the following paths C:(a) x=2t^2, y=t, z=t^3 from t=0 to t=1; (b) the straight lines that A ·…

A: We will use parameterization to find line integral

Q: Verify that fy = fx ху ух f (x, y) = 2x'y' -x'y b. f(x,y)=(x' + y²)° а.

A:

Q: Find the extrema and/or the saddle points of the functions. a) f(x, y) = 9 - 2x + 4y − x² − 4y²

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Please explain how they get y_p(t) = Be^-t and everything after that. just dont understand the…

A:

Q: 2. Let closed curve C consist of the line segment from (0,0) to (2, 1), followed by the line segment…

A: We will solve both the parts using the basics of integral calculus, in particular double integral,…

Q: Determine the interval where b must belong so that the function f(x,y)=x^(2)+bxy+y^(2)−b^(2)x−2by…

A: We are given, f(x,y)=x2+bxy+y2-b2y-2by..............(1) and x2+y2<925................(2) We need…

Q: ди ди + x - Əx %| ду 0 =

A:

Q: af of H.W: Find and for the functions: b əx ду 1. f(x, y) = (xy-1)² 3. f(x, y) = (x²-1)(y + 2)…

A: Given functions are 1. f(x, y)=(xy-1)2 3. f(x, y)=(x2-1)(y+2) 4. f(x, y)=x(x2+y2)   To Find: ∂f∂x…

Q: az and ax az 6x3 3. Calculate the partial derivatives for the function z = - x3+3y3 み=…

A: We know that; The Quotient rule: fg'=f'·g-f·g'g2   3). Given: z=6x3x3+3y3

Q: Q4 A) Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A: The objective of the question is to verify the hypothesis of the Cauchy Picard theorem for the given…

Q: Calculate Vf, V•f, V×f f (x,y. =)= xi+ y'j-* by the function

A: Introduction: The curl of the vector f(x,y,z)=fxi+fyj+fzk is given by ∇×f=∂∂xi+∂∂yj+∂∂zk×fxi+fyj+fzk…

Q: A) Integrate f(x, y) = xy^2 over the square bounded with endpoints at (0, 0), (0, 1), (1, 0) and (1,…

A:

Q: Calculate the total effect of the wind  (W(x,y))  = ) along the path which is out the line  Y = 9x…

A: Given the vector field wx,y=ycosxy,xcosxy. Consider the path y=9x, x∈0,3. Let us parametrize the…

Q: Find the local linear approximation to f(x, y) = 4x² + y² at P(2,3)

A: We have to find the linear approximation of above function at (2,3) please see the explanation…

Q: 5y" — (y')¹ = y³ sinx

A: The given problem is to find dependent variable, independent variable, type , order ,degree and…

Q: Let f(x, y, z) = xyz Find the direction in which the function increase most rapidly at the point…

A: Given: fx,y,z=xy2z3 The gradient of a function if given by ∇f(x,y,z) =∂f∂x,∂f∂y,∂f∂z.

Q: f (x, y) = xª – 2.x² + y² – 4y + 5. a) Use the second derivative test to find the critical points b)…

A:

Q: 1. v₁ = (4, −2, 6, −4), V₂ = (6, −3, 9, −6)

A:

Q: Find the line integral of ​f(x,y,z)=x+y+z over the​ straight-line segment from ​(5,4,2) to (4,2,-2)

A: Note:- Since you asked multiple question ,according to our policy we can solve only first question…

Q: Find the first partial derivatives of 2х — у f(x, y) = 2x + у of Әх -(3,4) = of -(3,4) = ду at the…

A: To find the first partial derivatives of

Q: Integrate f(x, y) = 2x over curve C given that C is the part of y = 2x^2 from (2, 8) to (

A:

Q: Consider the following function: H(x, y) 7x'y +-21x'y Find the linear approximation of H(x, y)…

A:

Q: Find the Linearizat ion of Non lineah Relations hip Y= (ax+

A: This is the problem of linearization, application of differential calculus.

Q: Q2/A/<he di fferential equation is yedx +3xay+dx +dyno diff erential when fineling the solution to a…

A: To find: The solution of differential equation y2dx+3x2y2dx+dy=0 and also find the constant (c) at a…

Q: Given Yy - y = – ỹ Yy - y + y. - ỹ and (y — У )? [(Yj – J,) + ỹ, – ỹ )]² 2. %3D

A: Given that

Q: At what interval is y=2x4- 4x2 concave downward? Ux> 3 3 3 3 V3 3 <x< 3 3 <x< V

A:

Q: Find the direction of maximum change of f(x, y, z) = xey + z² at (1, In 2,2).

A: Introduction: A function's maximum directional derivatives at a particular point P are produced in…