(ди a?u 0 0 at ax2 u(0,t) = U1, u(x, 0) = f(x), u(L, t) = U2 ,t > 0 0
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Determine a formal solution of the heat flow problem described by the following initial-value and boundary problem
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- Tangent to the curve z2 =2xy + x2, z= 3, at the point ( 1, 4,3)A heat-seeking particle is located at the point (2, −2) on a metal plate whose temperature at (x,y) is T(x, y) = 10 − x^2 − y^2. Find the path of the particle as it continuously moves in the direction of maximum temperature increase.Resolver por transformada de laplace Y"+4y=cosx. Y(0)=1 y'(0)=1
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- The temperature at any point (x, y) in a steel plate is T = 500 − 0.6x2 − 1.2y2, where x and y are measured in meters. At the point (7, 6), find the rates of change of the temperature with respect to the distances moved along the plate in the directions of the x- and y-axes. ∂T ∂x (7, 6) = °/m ∂T ∂y (7, 6) = °/mExplain of the method of proving the derivative (dy/dx) of y= U(x)V(x) where U(x)and V(x) are differential function of (x) , with two examples?Explain of the method of proving the derivative (dy/dx) of y=U(x)ᵛ⁽ˣ⁾ where U(x) and V(x) are differential function of (x), with two examples ?