Solving a Partial Differential Equation

YongL
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A partial differential equation.
 

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It is the Laplace equation in cylindrical coordinates with symmetry about y-axe.
You can solve it by variable separation, once given the boundary condition:
phi(x,y)=X(x)Y(y)

X''+X'/x+cX=0 (in x, 0-order Bessel equation)
Y''-cY=0 (in y)
c=arbitrary positive/negative real constant
 
Thanks, roberto, i got it
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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