5. Consider the heat problem that is described by: 0.9urr = Ut; 0 < x < 5, t > 0 и (0, t) — 0, и(5, t) — 0, t>0 u(x, 0) = 5x – x² 0 < x < 5 (a) Identify the heat diffusivity constant a2, the length of the bar L, and the initial temperature distribution f(x). (b) Plug a2 and L into u(x, t) to describe the solutions to this problem. u(x, t) = £ -a²n²n² Cne sin n=1

Q: 12. G(T) Jtan r G(x) = | ; dt et +3 tan x

A: Given,  G(x)=∫tan x1etet+3dt

Q: x² (y + z) – 4V/x²+ y² + z² = 0,

A:

Q: Consider the heat problem that is described by: 0.9urr = Ut, 0 0 u(0, t) = 0, u(5, t) = 0, t>0 u(x,…

A:

Q: Find dw/ds and ðw/at using the appropriate Chain Rule. Function Values w = sin(4x + 5y) x = s + t, y…

A:

Q: A rod has a temperature distribution according to function f(x) on it initially. The boundary…

A:

Q: Solve Laplace's equation inside the quarter-circle of radius 1, where we have a perfectly insu-…

A:

Q: 20. Let h be the function defined by h(x) = [", sin²r dt. Which of the following is an equation for…

A:

Q: - (0) A +x= ES

A:

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.