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7. (a) What is the solution method called that converts a semilinear first order PDE into an ODE system, solves that, eliminates the ODE independent variable, and eliminates the constants of integration to finally formulate the general solution of the PDE? (b) Which kind of first order PDE will allow to express u explicitly from the general solution that involves an arbitrary function? (c) Which one of the following two solutions is called right-travelling wave and which is called left- travelling wave? u(x, t) = G(r+ ct), e>0: u(x, t) = F(r - t), c>0:

7. (a) What is the solution method called that converts a semilinear first order PDE into an ODE system, solves that, eliminates the ODE independent variable, and eliminates the constants of integration to finally formulate the general solution of the PDE? (b) Which kind of first order PDE will allow to express u explicitly from the general solution that involves an arbitrary function? (c) Which one of the following two solutions is called right-travelling wave and which is called left- travelling wave? u(x, t) = G(r+ ct), e>0: u(x, t) = F(r - t), c>0:

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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this is all one question. topic is partial differential equations
 
7. (a) What is the solution method called that converts a semilinear first order PDE into an ODE system, solves that, eliminates the ODE independent variable, and eliminates the constants of integration to finally formulate the general solution of the PDE? (b) Which kind of first order PDE will allow to express u explicitly from the general solution that involves an arbitrary function? (c) Which one of the following two solutions is called right-travelling wave and which is called left- travelling wave? u(r, t) = G(r + ct), c>0: u(r, t) = F(r- ct), c>0: (d) Which kind of conditions are used to fix the arbitrary function in the general solution of the PDE?
Transcribed Image Text:7. (a) What is the solution method called that converts a semilinear first order PDE into an ODE system, solves that, eliminates the ODE independent variable, and eliminates the constants of integration to finally formulate the general solution of the PDE? (b) Which kind of first order PDE will allow to express u explicitly from the general solution that involves an arbitrary function? (c) Which one of the following two solutions is called right-travelling wave and which is called left- travelling wave? u(r, t) = G(r + ct), c>0: u(r, t) = F(r- ct), c>0: (d) Which kind of conditions are used to fix the arbitrary function in the general solution of the PDE?
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