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A Bernoulli differential equation is one of the form dy/dx + P(x)y =Q(x)y^n. 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 (du/dx) + (1-n)P(x)u=(1-n)Q(x). Use an appropriate substitution to solve the equation xy'+y=6xy^2,

A Bernoulli differential equation is one of the form dy/dx + P(x)y =Q(x)y^n. 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 (du/dx) + (1-n)P(x)u=(1-n)Q(x). Use an appropriate substitution to solve the equation xy'+y=6xy^2,

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 + P(x)y =Q(x)y^n.

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

(du/dx) + (1-n)P(x)u=(1-n)Q(x).

Use an appropriate substitution to solve the equation

xy'+y=6xy^2,

and find the solution that satisfies y(1)=8.

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