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Observe that, if n = the substitution u = y¹ equation dy dx 0 or 1, the Bernoulli equation is linear. For other values of n, transforms the Bernoulli equation into the linear du d.x + P(x)y= Q(x)y". + (1 − n)P(x)u = (1 − n)Q(x). Use an appropriate substitution to solve the equation y³ 3 y' --Y = I and find the solution that satisfies y(1) = 1. y(x) x5

Observe that, if n = the substitution u = y¹ equation dy dx 0 or 1, the Bernoulli equation is linear. For other values of n, transforms the Bernoulli equation into the linear du d.x + P(x)y= Q(x)y". + (1 − n)P(x)u = (1 − n)Q(x). Use an appropriate substitution to solve the equation y³ 3 y' --Y = I and find the solution that satisfies y(1) = 1. y(x) x5

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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dy dx du dx + P(x)y= Q(x)y". Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y¹ transforms the Bernoulli equation into the linear equation + (1 − n)P(x)u = (1 − n)Q(x). Use an appropriate substitution to solve the equation y³ x5 3 y' --Y = I and find the solution that satisfies y(1) = 1. y(x)
Transcribed Image Text:dy dx du dx + P(x)y= Q(x)y". Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y¹ transforms the Bernoulli equation into the linear equation + (1 − n)P(x)u = (1 − n)Q(x). Use an appropriate substitution to solve the equation y³ x5 3 y' --Y = I and find the solution that satisfies y(1) = 1. y(x)
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