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Use an appropriate substitution to solve the equation 7 y y = x20 and find the solution that satisfies y(1) = 1. y(x) = 4(9x^28)/(-4x^9 +9(13/9)))^0.5

Use an appropriate substitution to solve the equation 7 y y = x20 and find the solution that satisfies y(1) = 1. y(x) = 4(9x^28)/(-4x^9 +9(13/9)))^0.5

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 + P(x)y = Q(x)y". dx Observe that, if n = O 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 - п)Р(x)и — (1 - п)О(х). dx Use an appropriate substitution to solve the equation 7 y y = x20 ' and find the solution that satisfies y(1) = 1. y(x) = 4(9x^28)/(-4x^9 +9(13/9)))^0.5
Transcribed Image Text:A Bernoulli differential equation is one of the form dy + P(x)y = Q(x)y". dx Observe that, if n = O 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 - п)Р(x)и — (1 - п)О(х). dx Use an appropriate substitution to solve the equation 7 y y = x20 ' and find the solution that satisfies y(1) = 1. y(x) = 4(9x^28)/(-4x^9 +9(13/9)))^0.5
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