Thread: Need help in Homogeneous equation ...

Hi.
first i apologize for my bad english.

I need to solve this equation : ( i have its solution but can't understand some parts of it )

(y⁴ - 3x²)dy + xydx = 0 (1)

I use y = t^a ــ> dy = at^a-1dt (2) and place it in (1) :

a(t^5a-1 - 3x²t^a-1)dt + xt^adx = 0

then i don't understand this next part ( I'm typing it from solution of problem ): 5a - 1 = 2 + a - 1 ?
it then calculates a = 1/2 and solves the equation ... i don't get why 5a - 1 = 2 + a - 1 ...
thanks in advance.

Hey mhmarefat.

Is this a Bernoulli type DE?