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A Bernoulli differential equation is one of the form dy dx Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u transforms the Bernoulli equation into the linear equation = yl-n du dx + P(x)y = Q(x)y”. + (1 − n)P(x)u = (1 − n)Q(x). - Use an appropriate substitution to solve the equation xy' + y = −9xy², and find the solution that satisfies y(1) = −7. y(x) = 4/(x+36xln(x))

A Bernoulli differential equation is one of the form dy dx Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u transforms the Bernoulli equation into the linear equation = yl-n du dx + P(x)y = Q(x)y”. + (1 − n)P(x)u = (1 − n)Q(x). - Use an appropriate substitution to solve the equation xy' + y = −9xy², and find the solution that satisfies y(1) = −7. y(x) = 4/(x+36xln(x))

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
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A Bernoulli differential equation is one of the form dy dx Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u transforms the Bernoulli equation into the linear equation = yl-n du dx + P(x)y = Q(x)y”. + (1 − n)P(x)u = (1 − n)Q(x). Use an appropriate substitution to solve the equation xy' + y = −9xy², and find the solution that satisfies y(1) = −7. y(x) = 4/(x+36xln(x))
Transcribed Image Text:A Bernoulli differential equation is one of the form dy dx Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u transforms the Bernoulli equation into the linear equation = yl-n du dx + P(x)y = Q(x)y”. + (1 − n)P(x)u = (1 − n)Q(x). Use an appropriate substitution to solve the equation xy' + y = −9xy², and find the solution that satisfies y(1) = −7. y(x) = 4/(x+36xln(x))
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