def ode_Bernoulli(eq, func, order, match):
 x = func.args[0]
 f = func.func
 r = match
 C1 = get_numbered_constants(eq, num=1)
 t = exp(((1 - r[r['n']]) * Integral((r[r['b']] / r[r['a']]), x)))
 tt = ((r[r['n']] - 1) * Integral(((t * r[r['c']]) / r[r['a']]), x))
 return Eq(f(x), (((tt + C1) / t) ** (1 / (1 - r[r['n']]))))

def ode_Bernoulli ( eq , func , order , match ) : x = func . args [ 0 ] f = func . func r = match C1 = get_numbered_constants ( eq , num = 1 ) t = exp ( ( ( 1 - r [ r [ 'n' ] ] ) * Integral ( ( r [ r [ 'b' ] ] / r [ r [ 'a' ] ] ) , x ) ) ) tt = ( ( r [ r [ 'n' ] ] - 1 ) * Integral ( ( ( t * r [ r [ 'c' ] ] ) / r [ r [ 'a' ] ] ) , x ) ) return Eq ( f ( x ) , ( ( ( tt + C1 ) / t ) ** ( 1 / ( 1 - r [ r [ 'n' ] ] ) ) ) )
solves bernoulli differential equations .