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
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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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