A partial differential equation

[Navid555]

Hello. I have two questions about this differential equation :
1.is this homogeneous?
2.how can I solve? (can I solve It with separation method?)

 

[Deleted member 4993]

Hello. I have two quastion about this diffrential equation :
1.is this hemogenios?
2.how can I solve? (can I solve It with seperation method?)

View attachment 32776

The leftHandSide of the PDE is function of x &y and the rightHandSide is a function of 't'. So, if x and y are not function of 't' (in general those are orthogonal to each other) then we can write both LHS and RHS to be equal to a constant 'K'.

Since that "constant" can be any number, NOT necessarily equal to zero, the whole PDE is NOT 'homogeneous'.

Yes - you start to solve it through separation of variable like:

T(x,y) = G(x) * H(y)

 

[Navid555]

Thank you for your help. I use seperation method to solve the equation that is in the picture. But nonhemogenios term prevents seperation. Should I solve hemogenios form of this equation first? How can I solve nonhemogenios part of this problem?

The leftHandSide of the PDE is function of x &y and the rightHandSide is a function of 't'. So, if x and y are not function of 't' (in general those are orthogonal to each other) then we can write both LHS and RHS to be equal to a constant 'K'.

Since that "constant" can be any number, NOT necessarily equal to zero, the whole PDE is NOT 'homogeneous'.

Yes - you start to solve it through separation of variable like:

T(x,y) = G(x) * H(y)

 

[Deleted member 4993]

Thank you for your help. I use seperation method to solve the equation that is in the picture. But nonhemogenios term prevents seperation. Should I solve hemogenios form of this equation first? How can I solve nonhemogenios part of this problem?

If this problem is an assignment in a course-work, you must have been shown the solution of

unsteady-state-heat-transfer-equation in 2-D space.

Follow the same procedure. You could Google the term s above, and te tell us what you found.