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Posted on 2014-04-24

I reading the solution of a dif eq

Y'' -m^2 *n^2 * y =

Y = c1e1 ^ ( -mny) + c2e2 ^ ( + mny )

how did he get this result ?

and X'' + n^2X

then X = c3 sin nx + c4 cosnx

Y'' -m^2 *n^2 * y =

Y = c1e1 ^ ( -mny) + c2e2 ^ ( + mny )

how did he get this result ?

and X'' + n^2X

then X = c3 sin nx + c4 cosnx

4 Comments

I still might not be able to help, but the text form of complex math is an additional and unpleasant hurdle.

A*b*b*exp(bt) + n²*A*exp(bt) = 0

and this can only be so if b²=-n² and this only if b = i*n where i is the square root of -1.

(Because e to the power of anyting is NEVER zero, and A=0 is a tribial solution)

And n can be positive of negative, since it square is aloways positive, so the exponentials are exp(int) and exp(-int), and it you remember your trig, this is sin(nt) and cos(nt) and hence the result.

So back into the first equation where n² is m²*n² and presto the result.

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