Let u be the general solution of Heat Equation: u, = uxA) Show that the general solution of the cable equation:v = ver - av,with a > 0, is given by: v(x, t) = e "u(x,t),B) Let v be the general solution of the convection-diffusion equation: v, = v -cv, , with c > 0. Show thatu(x, t) = v(x + ct, t)

Let u be the general solution of Heat Equation ut=uxx (i) To…

Let u be the general solution of Heat Equation: u, = ux: A) Show that the general solution of the cable equation: with a > 0, is given by: v(x, t) v, = vr – av, = e ""u(x,t), B) Let v be the general solution of the convection-diffusion equation: v, = vx with c >0. Show that u(x, t) = v(x + ct, t) %3D

Let u be the general solution of Heat Equation: u, = ux: A) Show that the general solution of the cable equation: with a > 0, is given by: v(x, t) v, = vr – av, = e ""u(x,t), B) Let v be the general solution of the convection-diffusion equation: v, = vx with c >0. Show that u(x, t) = v(x + ct, t) %3D

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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