Solution of the 2nd-order pde u_t=u_xy

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SUMMARY

The second-order partial differential equation (PDE) u_t = u_xy is a rotated version of the heat equation. This equation has been studied in the literature, and resources on the heat equation can provide insights into its general solution. To proceed with solving this PDE, one should explore techniques specific to the heat equation and its transformations.

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  • Understanding of partial differential equations
  • Familiarity with the heat equation
  • Knowledge of solution techniques for linear PDEs
  • Basic concepts of mathematical transformations
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  • Research the heat equation and its properties
  • Explore methods for solving linear PDEs, such as separation of variables
  • Study literature on transformations of PDEs
  • Investigate numerical methods for approximating solutions to PDEs
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Mathematicians, physicists, and engineers working with partial differential equations, particularly those interested in thermal dynamics and mathematical modeling.

pep2010
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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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