Question: how to solve y = y a , y ( 0 ) , = 0 where 0 < a < 1 some constant with the

how to solvey=ya,y(0),=0 where0<a<1 some constant with the method of separation of variables? The solution should bex(t)=sgn(t)((1a)t)1/(1a) but I can't deduce it rigorously with separation of variables.

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