- #1

gtfitzpatrick

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## Homework Statement

determine the char. curve and gen. sol. for x[tex]^{3}[/tex] [itex]

\frac{\partial{u}}{\partial{x}}

[/itex] - [itex]

\frac{\partial{u}}{\partial{y}}

[/itex] = 0

## Homework Equations

find sol and domain of influence when u(x,0) = [tex] \frac{1}{1+x^2} [/tex]

show sol is not defined when y> [tex] \frac{1}{2x^2} [/tex]

## The Attempt at a Solution

so [tex] \frac{\partial{y}}{\partial{x}} = \frac{-1}{x^3} [/tex]

and [tex] \frac{\partial{u}}{\partial{x}} = 0 [/tex]

which gives u(x,y) = [tex]F( \frac{1}{2x^2} - y) [/tex] is the gen solution right?

then sol. at u(x,0) = [tex] \frac{1}{1+x^2} [/tex]

[tex] \frac{1}{1+x^2} [/tex] = [tex]F( \frac{1}{2x^2} - y) [/tex]

= [tex]F( \frac{1}{2x^2}) [/tex]

which gives x = +/- 1 am i right in this? and how do i find domain of influnce?