A Nice Differential Equation

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[@rajeshbuya]

e^iπx can be written further as (-1)^x
So in your 1st method, the solution can be further written as
y = k.(-1)^x

[@SweetSorrow777]

Easy separable differential equation.

[@giuseppemalaguti435]

Ah ah...why nice???

[@marzipanhoplite17]

For x integer we get only the real part of re^iπχ and if it is an even integer we get r, if it is an odd integer we get -r. It seems that this kind of differential equation is somehow symmetric in this case

[@Blaqjaqshellaq]

If you graph the real and imaginary coefficients of y, you get a circle centred at 0 with radius |r|.

[@mashalrazavi579]

Tnx but very easy

[@seroujghazarian6343]

y=ke^(iπx)

[@scottleung9587]

I used the first method.