A) Classify and find general expressions for the characteristic coordinates for the equation {see attachment}
b) Use the canonical coordinates {see attachment} and transfer the above PDE into the new coordinates. Solve it in the new coordinates and show that {see attachments} where F and G are arbitrary functions of their arguments.

a) Classify and find general expressions for the characteristic coordinates for the equation

( 1)

b) Use the canonical coordinates and and transfer the above PDE into the new coordinates. Solve it in the new coordinates and show that

where F and G are arbitrary functions of their arguments.

Solution:
a) The quadratic terms of the equation (1) are:

The corresponding characteristic equation is:
( 2)
( 3)
Since , the PDE is of hyperbolic type and ...

Solution Summary

This shows how to classify and find general expressions for characteristic coordinates and use given canonical coordinates to transfer a partial differential equation to new coordinates.

Find the region in the xy plane in which the equation [(x - y)^2 - 1] u_xx + 2u_xy + [(x - y)^2 - 1] u_yy = 0 is hyperbolic. The complete problem is in the attached file.

Please help with the following problem. Provide step by step calculations for each problem.
Consider the Helmholtz partialdifferential equation:
u subscript (xx) + u subscript (yy) +(k^2)(u) =0
Where u(x,y) is a function of two variables, and k is a positive constant.
a) By putting u(x,y)=f(x)g(y), derive ordinary diff

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Non- Homogeneous Linear PartialDifferential Equation with Constant Coefficients
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Hi,
Please help working on
section 1.1 problems 2,4,8,14,16
section 1.2 problems 6,10,20,24,27
thank you
See attached
Classify each as an ordinary differential equation (ODE) or a partialdifferential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ODE, ind

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Eliminate the arbitrary constants from the equation: y = Ae^x + Be^2x + Ce^3x. Make sure to show all of the steps which are involved.

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(2) Use Laplace Transforms to solve Differential Equation
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Note: To see the questions in their mathematic

1) Let A(x,y) be the area of a rectangle not degenerated of dimensions x and y, in a way that the rectangle is inside a circle of a radius of 10. Determine the domain and the range of this function.
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I am asking for the step-by-step workings for all of the attached problems.
** Please see the attached file for complete problem description **
1st problems. Please find the general solution of:
(1) dy/dx = y/sin(y) - x
(2) dy/dx = y + cos(x)y^2010
In the process of finding the solutions for the problems make use of both