Idealistic
Junior Member
- Joined
- Sep 7, 2007
- Messages
- 97
**Note: ux = du/dx; uy = du/dy where u = u(x,y)**
Solve aux+ buy= f(x, y), where f(x, y) is a given function. Write the
solution in the form:
u(x, y) = (a2 + b2)1/2 Integral(L)fds + g(bx -ay)
Where L is the characteristic line segment from the y axis to the point (x,y). There's also a hint to use the coordinate method.
heres what I have:
x' = ax + by; y' = bx - ay
aux + buy = a(aux' + buy') + b(bux' - auy') = (a2+b2)ux' = f(x',y')
ux' = (a2+b2)-1f(x',y')
I understand with a line integral we have to come up with an equation that parametrizes f(x',y') with a funtion r(t). So if its a point from the y axis (x = 0 y = y1) to the point (x = x2, y = y2) what does that mean for our new variables x' and y'? (x', y') = ?? and also, how can I determine a simple r(t) funciton with all of these change of variables.
Solve aux+ buy= f(x, y), where f(x, y) is a given function. Write the
solution in the form:
u(x, y) = (a2 + b2)1/2 Integral(L)fds + g(bx -ay)
Where L is the characteristic line segment from the y axis to the point (x,y). There's also a hint to use the coordinate method.
heres what I have:
x' = ax + by; y' = bx - ay
aux + buy = a(aux' + buy') + b(bux' - auy') = (a2+b2)ux' = f(x',y')
ux' = (a2+b2)-1f(x',y')
I understand with a line integral we have to come up with an equation that parametrizes f(x',y') with a funtion r(t). So if its a point from the y axis (x = 0 y = y1) to the point (x = x2, y = y2) what does that mean for our new variables x' and y'? (x', y') = ?? and also, how can I determine a simple r(t) funciton with all of these change of variables.