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A Bernoulli differential equation (named after James Bernoulli) is of the form
dy / dx + P(x) y = Q(x)yn
Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, show that the substitution u = y1-n transforms the Bernoulli equation into the linear equation
dy / dx + 1 (1 - n) P(x) u = (1 - n) = Q(x) |
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