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Partial Differential equations

1.(a) Find characteristics for the PDE describing u(t, x) for t ∈ R and x ∈ R
Hence find the general solution.
(b) Find the solution that satisfies the initial conditions
 
  
2. Consider the following equation for u(x,y)
  (a) Assuming x 6=0classify this equation and show that its characteristic equations are given by
 
  
(b) Use these characteristics to show that the equation reduces to the standard form:
   (c) Hence find the general solution for u(x,y).
 
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can be obtained by letting E(x,t) = v(t)U (x,t)with a view to removing the first order time derivative.Use this process to obtain the Klein-Gordon equation,
  

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More MX3536 MX3536 Differential Equations: Questions & Answers

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Management

Some integrations look simple but turn out to be quite involved. Question 1 covers such a situation. In such questions it can help to split the working into two vertical columns, with the main integration being dealt with in the LH column and the substitution working being dealt with in the RH colum ...

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BBMP1103 Mathematics for Management

Question 1Given the following equation:x + y + z = -5x – 4y + z = 35x + 3y + 4z = -18 i. Form a matrix from the given equation( 5 )ii. Determine the determinant( 5 )iii. Find an inverse matrix( 5 )iv. Find solutions using Cramer’s rule ...

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Methods and Analysis System

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Show your work and note the rounding and accuracy requirement for each problem. 1.Karim works in a retail computer store. He receives a weekly base salary of $400 plus a commission of 3% of sales exceeding his quota of $25,000 per week. What are his total sales for a week in which he earns $730.38? ...

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