Q3. Consider the following boundary and initial conditions and solve the given partial differential equation using the separation of variables method a?u a²u = 4 at? ax2 u(0, t) = 0 for t> 0 u(4, t) = 0 for t>0 ди (х.0) for 0sxs4 at u(x,0) : for 0sxs4 3

Q3. Consider the following boundary and initial conditions and solve the given partial differential equation using the separation of variables method a?u a²u = 4 at? ax2 u(0, t) = 0 for t> 0 u(4, t) = 0 for t>0 ди (х.0) for 0sxs4 at u(x,0) : for 0sxs4 3

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Q3. Consider the following boundary and initial conditions and solve the given
partial differential equation using the separation of variables method
a?u
= 4
at?
a?u
ax2
и(0, t) 3D о
for
t > 0
u(4, t) = 0
for
t > 0
ди (х,0)
= 0
at
for 0sxs4
u(x, 0) =
for 0sx< 4
3

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