A Bernoulli differential equation is one of the form dy + P(x)y = Q(x)y". dr Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y!n transforms the Bernoulli equation into the linear equation du + (1 – n)P(x)u = (1 – n)Q(x). dx Use an appropriate substitution to solve the equation xy' + y = 9xy?, and find the solution that satisfies y(1) = -4. y(x) =

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A Bernoulli differential equation is one of the form
dy
+ P(x)y = Q(x)y".
dr
Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y!n
transforms the Bernoulli equation into the linear equation
du
+ (1 – n)P(x)u = (1 – n)Q(x).
dx
Use an appropriate substitution to solve the equation
xy' + y = 9xy?,
and find the solution that satisfies y(1) = -4.
y(x) =
Transcribed Image Text:A Bernoulli differential equation is one of the form dy + P(x)y = Q(x)y". dr Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y!n transforms the Bernoulli equation into the linear equation du + (1 – n)P(x)u = (1 – n)Q(x). dx Use an appropriate substitution to solve the equation xy' + y = 9xy?, and find the solution that satisfies y(1) = -4. y(x) =
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