A Bernoulli differential equation is one of the form Observe that, if n 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = Use an appropriate substitution to solve the equation and find the solution that satisfies y(1) = 1. y(x) = dy + P(x)y = Q(x)y". dx y¹ transforms the Bernoulli equation into the linear equation du + (1 − n)P(x)u = (1 − n)Q(x). dx Y' 2 x y= 34 2.3

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