Solve the following boundary value problem by the method of Separation of variables au 4 at ,U(0, t) = 20, U (1T, t) = 40, U(x, 0) = 50,0

Q: 6x2+7y2=C satisfies 6x+7yy' given the inital condition y=4 when x=6 what is C.

A:

Q: Consider the boundary-value problem. y" - xy = 1, y (0) = 1, 0≤x≤ 1 y(1) = 0. Use the linear finite…

A:

Q: If the critical point of the function f (x, y) = x - y - 2xy + 6 is (0.0), test this point whether…

A: Given function is fx,y=x3-y3-2xy+6 and the point is (0.0) Test the point

Q: Let f(x, y) = 3x²y + y³ - 3x² - 3y² + 2. Find all the critical points.

A: fx, y=3x2y+y3-3x2-3y2+2 We have to find all critical points of the given function.

Q: Use the method of separation of variables to obtain solutions to the following boundary value…

A:

Q: 5) (xy² +x-2y+3) dx + x² ydy = 2(x+ y)dy when x = 1, y = 1

A:

Q: Z=8x+12y subject to 4x+6y>14 , 4x+5y > 9, x20, y20 x=? (2 decimal places) Minimize

A:

Q: a Find all critical points of z = (y- 3)(z+ 2y+ 7), = (y+z). Show work.

A: We have to find the critical points of the given equations. For the critical points find the…

Q: Construct a finite difference method to approximate the elliptic partial difference equation Uxx +…

A:

Q: Determine the absolute maximum and minimum values of f(x, y) = 2x² + 3y² on the rectangular region…

A:

Q: 4Ux+Uy=U² , U(x,0)=1/1+x²

A: In the given partial differential equation with the given initial condition. 4ux+uy=u2u(x,0)=11+x2

Q: Consider y" + 4y' + 5y = ae -3* 8 (t - 31), y (0) = 1, y (0) = -2. Зл Find the value of a such that…

A:

Q: 1 Find the points of discontinuity of y = where и +и - 2 1 u = * - 1

A:

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

A:

Q: 2 Compute dy for x=4t³_t²+7t y=t"-6

A:

Q: 9. The average revenue function of x units of product is R(x)=-mx+n,where m and n are constants. a)…

A: Given that: Average revenue function, R¯(x)=-mx+n

Q: Lây ởy - Find the bounded solution of- ,x>0, t> 0 where y (0, t) = 1, y (x, 0) = 0.

A:

Q: Find the maximum value of f(x, y, z) = y - z Subject to x + y + z = 1,x² + y² = 1 O - √5 + 1 O-√5-1…

A:

Q: What is the maximum rate of change of ƒ(x, y) = x² + y² at the point (1,0) ○ (2,0) 2x + 2y 4x² + 4y²…

A:

Q: Find the bounded อน əx solution of อน 2 + U if U(x, 0) = 6e-3x. at

A: We have ∂u∂x=2∂u∂t+u  The initial condition is ux,0=6e-3x Now, ∂u∂x=2∂u∂t+u can be written as…

Q: 7. Integrate * m Note: fedu = e² + C Ox²ex-2xe* + 2e* + C O-tanx + C 4 O x² + 2xe* - 2e* + C O x² -…

A:

Q: Let f(x, y) = x³ + 2ry – y² be a func the tangent plane to f(x, y) at the poi

A: Here we have f(x,y)=x3+2xy-y2  we have to find the equation of the tangent plane to f(x,y) at point…

Q: Compute the maximum value of the utility function U(x,y, z) = xyz, subject to x+ 3y+4z 60. %3D

A: To find: Maximum of the function U(x,y,z)=xyz subject to x+3y+4z=60.

Q: What are the critical points of the function f (x, y) = cosh(x + 1) + sin(ry)– ex+1)y on the line y…

A:

Q: Suppose that λ =A₁, A₂ are constants such that u(z,y) = F (z+ Ay) statisfied the PDE 82 -4 ( 5²2 U…

A: