Separate the following PDE as much as possible

Jozefina Gramatikova
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Homework Statement


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Homework Equations


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The Attempt at a Solution


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Could you tell me is there something specific that I need to the with sin(xy)? Thanks
 

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You can proceed with the method of separating variables and divide both sides by ##\alpha(x) \beta(y)##. Does it look like this equation is separable?
 
kuruman said:
You can proceed with the method of separating variables and divide both sides by ##\alpha(x) \beta(y)##. Does it look like this equation is separable?
Yeah it seems like this is not a separable equation :(
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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