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## Main Question or Discussion Point

hi..

with refrenence to http://www.math.uah.edu/howell/MAPH/Archives/Old_Notes/PDEs/PDE1.pdf [Broken]

page 7,

“Observe” that the only way we can have

here I do understand that for these to being equal requires them to be constant, because changing either t or x would affect either side of the formula breaking the inequality, so to be equal they are supposed to be a constant. (please correct me if i go wrong anywhere..)

Now what i am not sure about is that these two formulas can also be equal to each other for a specific value of x and t, is this anything to do with the constant that they will be equal to??

It is said that the constant say k is arbitrary, suggesting these two sides are equal for more than one value of x and y... how is this said?

(I gave the link so that i don't have to explain what i am asking, because i don't know the correct terms and that might turn confusing.. no copyright violation intended)

with refrenence to http://www.math.uah.edu/howell/MAPH/Archives/Old_Notes/PDEs/PDE1.pdf [Broken]

page 7,

“Observe” that the only way we can have

formula of t only= formula of x only

is for both sides to be equal to a single constant.here I do understand that for these to being equal requires them to be constant, because changing either t or x would affect either side of the formula breaking the inequality, so to be equal they are supposed to be a constant. (please correct me if i go wrong anywhere..)

Now what i am not sure about is that these two formulas can also be equal to each other for a specific value of x and t, is this anything to do with the constant that they will be equal to??

It is said that the constant say k is arbitrary, suggesting these two sides are equal for more than one value of x and y... how is this said?

(I gave the link so that i don't have to explain what i am asking, because i don't know the correct terms and that might turn confusing.. no copyright violation intended)

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