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Use an appropriate substitution to solve the equation xy' + y = -2xy², and find the solution that satisfies y(1) = 9.

Use an appropriate substitution to solve the equation xy' + y = -2xy², and find the solution that satisfies y(1) = 9.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A Bernoulli differential equation is one of the form dy dx -n Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y¹n transforms the Bernoulli equation into the linear equation + P(x)y = Q(x)y". du dx = + (1 − n)P(x)u = (1 − n)Q(x). - Use an appropriate substitution to solve the equation xy' + y = -2xy², and find the solution that satisfies y(1) = 9. y(x) =
Transcribed Image Text:A Bernoulli differential equation is one of the form dy dx -n Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y¹n transforms the Bernoulli equation into the linear equation + P(x)y = Q(x)y". du dx = + (1 − n)P(x)u = (1 − n)Q(x). - Use an appropriate substitution to solve the equation xy' + y = -2xy², and find the solution that satisfies y(1) = 9. y(x) =
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