Textbook 'Applied Partial Differential Equations Revised Edition' by Jhon Ockenden, Sam Howison, Andrew Lacey, and Alexander
a.)
Consider the given integrable function as
The integration can be separated as
Since is an even function, the first integral is
Since is an odd function, the second integral is
So the the integral we need to find is
b.)
Define .
By substituting the above transformations into the integral, we get
.
c.)
Let
Let us find the derivative of I with respect to z, i.e.,
Use the integration by parts to I, then we get
Solution of this first order ODE is
d.)
Define . Substitute these into the integral to get
The integral value is
Textbook 'Applied Partial Differential Equations Revised Edition' by Jhon Ockenden, Sam Howison, Andrew Lacey, and Alexander...
Hello! I need help answering these Partial Differential Equations exercises! Exercise 1 Find the general solution of the cquation ury(r, y) 0 in terms of wo arbitrary functions. Exercise 2 Verify that 2c9(s)ds tcontinuously differentiable function. Hint: Here you will need to use iz' ution to the wave equation u2S, where c is a constant and g is 1's rule for differentiating an integral with respect to a parameter that a given urs n the limits of integration: b(t) F(b(t))b'...
write MATLAB scripts to solve differential equations. Computing 1: ELE1053 Project 3E:Solving Differential Equations Project Principle Objective: Write MATLAB scripts to solve differential equations. Implementation: MatLab is an ideal environment for solving differential equations. Differential equations are a vital tool used by engineers to model, study and make predictions about the behavior of complex systems. It not only allows you to solve complex equations and systems of equations it also allows you to easily present the solutions in graphical form....
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I DESPERATELY NEED HELP WITH THIS DIFFERENTIAL EQUATIONS MATLAB ASSIGNMENT IM SUPPOSED TO BE LEARNING BUT WE HAVE A SUB AND HE DIDN'T TEACH IT! ITS EULER AND IMPROVED EULER IN MATLAB! HERE IS THE LINK FOR THE IMAGE FILE THAT SHOWS THE FULL INSTRUCTIONS FOR THE CODE. https://imgur.com/a/gjmypLs Also, here is my code so far that I borrowed form an old assignment but the data is all wrong and the application of the code is slightly different so either...
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By 5. (a) Verify that y = {24 sin x is a solution to the differential equation dx2 dy + 5y = 0. dc [10 marks) (b) Differentiate the following functions with respect to c: (i) In(1 + sin? 2) (ii) * 2x3 - 4 - 8 dc. (c) Evaluate the integral / 272 * +432 – 4.7" [15 marks] [25 marks] 6. (a) let f: R+R be a function defined by f(x) 3 + 4 if : 51 ax+b...
Need the following question answered, the subject is Mathematical Methods 2 (Mechanical Engineering). This is a University style question/practice paper with sections and I want the solutions to it, this comes with a formula sheet and if possible, use the formula sheet to answer the question. Need Calculations shown to each part of the question, My Teacher hasn't got back to me regarding the solutions so here I am, Thank you. Note: Please answer the question in UK style format...