Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation. dy y(xy° – 1) dx
Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation. dy y(xy° – 1) dx
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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Bernoulli's equation is a special type of first-order linear equation. Suppose a differential equation is given as
.
Then, the suitable transformation can convert this equation into the standard form of a first-order linear differential equation. We find the integrating factor. Then, on multiplying with the converted equation, we can find the solution in a new variable. Again, we replace the new variable with the old one. It leads to the final solution of the given differential equation.
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