Separation of variables The lateral radiation of heat from a bar of length L insulted at both ends can be modelled with the linear partial differential equation (PDE) du Pu = D -au for 00, 02² (1) Ət with the conditions ₂ (0,1)=₂(L,t)=0 and u(z,0)=f(x). where L.a, DER are positive constants. 1. Seek a separation solution of the form u(z,t) = X(z)T(t) to show +==k where & denotes the separation constant. ] 2. Use equation (2) to derive two ordinary differential equations (ODEs), one in spacer and one in time f. 3. Determine the boundary conditions for the ODE that depends on z.
Separation of variables The lateral radiation of heat from a bar of length L insulted at both ends can be modelled with the linear partial differential equation (PDE) du Pu = D -au for 00, 02² (1) Ət with the conditions ₂ (0,1)=₂(L,t)=0 and u(z,0)=f(x). where L.a, DER are positive constants. 1. Seek a separation solution of the form u(z,t) = X(z)T(t) to show +==k where & denotes the separation constant. ] 2. Use equation (2) to derive two ordinary differential equations (ODEs), one in spacer and one in time f. 3. Determine the boundary conditions for the ODE that depends on z.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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You need to solve only (3)part and solve plz perfectly i need perfect soloution take your time and give me 100 percent exact soloution. Plz
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