Solve (del^2 u) / (del x del t) = e^(-t) cos x given that u=0 when t=0 and del u/del t=0 @ x=0, also Show that u -> sin x as t -> infinity

## Problem

## Question

Solve (del^2 u) / (del x del t) = e^(-t) cos x given that u=0 when t=0 and del u/del t=0 @ x=0, also Show that u -> sin x as t -> infinity

## Topic

Solution of non-homogeneous Partial Differential Equation by direct integration

## Partial Differentiation Equation Problems

- Solve non-homogeneous Partial Differential Equation del^2 u/ del x^ 2 = x+y by direct integration
- Solve non-homogeneous Partial Differential Equation del ^2 z / (del x del y) = (x/y) + a by direct integration
- Solve non-homogeneous Partial Differential Equation (del^3 z) / (del x^2 del y) = cos(2x+3y) by direct integration
- Solve (del^2 z) / (del x del y) = sinx siny for which del z/del y = -2 sin y when x=0 and z=0 if ‘y’ is an odd multiple of PI/2 (or z=0 if y = (2n+1) PI/2)
- Solve (del^2 u) / (del x del t) = e^(-t) cos x given that u=0 when t=0 and del u/del t=0 @ x=0, also Show that u -> sin x as t -> infinity
- Solve del^2 z/ (del x^2) = xy subject to the condition that del z / del x = log (1+y) when x=1 and z=0 when x=0