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A Bernoulli differential equation is one of the form Use an appropriate substitution to solve the equation Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution uy-transforms the Bernoulli equation into the linear equation and find the solution that satisfies y(1) = 1. dy dz du dz + P(z)y = Q(z)y". + (1 − n)P(z)u = (1-n)Q(x).

A Bernoulli differential equation is one of the form Use an appropriate substitution to solve the equation Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution uy-transforms the Bernoulli equation into the linear equation and find the solution that satisfies y(1) = 1. dy dz du dz + P(z)y = Q(z)y". + (1 − n)P(z)u = (1-n)Q(x).

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 Use an appropriate substitution to solve the equation Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y ¹- -n transforms the Bernoulli equation into the linear equation and find the solution that satisfies y(1) = 1. y(x) = dy dx du dx + P(x)y= Q(x)y". + (1 − n)P(x)u = (1 − n)Q(x). y - 5 X ∙y = x4'
Transcribed Image Text:A Bernoulli differential equation is one of the form Use an appropriate substitution to solve the equation Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y ¹- -n transforms the Bernoulli equation into the linear equation and find the solution that satisfies y(1) = 1. y(x) = dy dx du dx + P(x)y= Q(x)y". + (1 − n)P(x)u = (1 − n)Q(x). y - 5 X ∙y = x4'
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