C2-solutions to a diff.equation.

  • Thread starter Hatmpatn
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  • #1
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I have the following problem:
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Calculate all the C2-solutions z(x,y) to the differential equation:

gRP2fyi.png


with the following constraint:
dQaYDIt.png

by making the substitution u=xy, v=x


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Solution
I've begun slightly but this doesn't take me far..

tLErcPB.png
 

Answers and Replies

  • #2
pasmith
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Start by working out what the differential operators [itex]\frac{\partial}{\partial x}[/itex] and [itex]\frac{\partial}{\partial y}[/itex] are in terms of [itex]u[/itex], [itex]v[/itex] and the differential operators [itex]\frac{\partial}{\partial u}[/itex] and [itex]\frac{\partial}{\partial v}[/itex]. From these you can find expressions for the second-order operators.

Now substitute these expressions into the original PDE, and tidy up the result. You should find that most of the terms cancel.
 

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