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#### blackthunder

##### New member

- Mar 18, 2012

- 3

Hi, need some help here so thanks to any replies.

PDE: $$yu_x+2xyu_y=y^2$$

edit: Forgot to mention the condition $$u(0,y)=y^2$$

a) characteristic equations:

$$dx/ds=y$$ $$dy/ds=2xy$$ $$du/ds=y^2$$

b) find dy/dx and solve

$$dy/dx=dy/ds * ds/dx = x/y$$

$$ydy=xdx$$

$$y^2/2=x^2/2 +c$$

$$y=\pm \sqrt{x^2+2c}$$

c) general solution

d) solve PDE

e) find u(x,y)

here I should be finding du/ds and solve after letting x(s)=? and y(s)=?

I need some help, so thanks guys.

PDE: $$yu_x+2xyu_y=y^2$$

edit: Forgot to mention the condition $$u(0,y)=y^2$$

a) characteristic equations:

$$dx/ds=y$$ $$dy/ds=2xy$$ $$du/ds=y^2$$

b) find dy/dx and solve

$$dy/dx=dy/ds * ds/dx = x/y$$

$$ydy=xdx$$

$$y^2/2=x^2/2 +c$$

$$y=\pm \sqrt{x^2+2c}$$

c) general solution

d) solve PDE

e) find u(x,y)

here I should be finding du/ds and solve after letting x(s)=? and y(s)=?

I need some help, so thanks guys.

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