Solution of the 2nd-order pde u_t=u_xy

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hey guys,

i've reduced a more complex pde to the second-order linear equation u_t=u_xy, but now I'm a bit stuck!

firstly, does anyone know if this equation has a proper name and thus been studied somewhere in the literature?

secondly, any ideas on how to proceed with the general solution?

cheers, pep2010
 
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This a rotated version of the heat equation. Check for that one
 
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