Explore BrainMass
Share

Solving Partial Differential Equations

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

Please see the attached file for the fully formatted problems.

1. Solve

u(0,t) = u(,t) =0

u(x,0) = xsinx ,

© BrainMass Inc. brainmass.com October 24, 2018, 9:07 pm ad1c9bdddf
https://brainmass.com/math/partial-differential-equations/solving-partial-differential-equations-117456

Attachments

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

1. Solve

u(0,t) = u(,t) =0

u(x,0) = xsinx ,

We start by setting the function u(x,t) as a product of a single-variable functions:

Therefore the partial derivatives become:

Plugging it back into the equation, one obtains:

Dividing by separates the equation:

Since both sides are totally independent (each is a function of an ...

Solution Summary

A PDE is solved. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

$2.19
See Also This Related BrainMass Solution

Solving Partial Differential Equations by Change of Variables

In solving this problem, derive the general solution of the given equation by using an appropriate change of variables.

1. ∂u/∂t - 2 ∂u/∂x = 2

Answer: u(x,t) = f(x + 2t) - x

In this exercise, (a) solve the given equation by the method of characteristic curves, and (b) check you answer by plugging it back into the equation.

2. ∂u/∂x + x2 ∂u/∂y = 0

Answer: (a) u(x,y) = f(1/3 x3 - y)

View Full Posting Details