- #1

Ultra

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Hello guys I hope you all are doing well. :)

I found below question in a book by Martin Braun "Differential Equations and Their Applications An Introduction to Applied Mathematics (Fourth Edition)"

The question :

The Bernoulli differential equation is (dy/dt)+a(t)y=b(t)y^n. Multiplying through by µ(t)=exp(Integral of a(t).dt), we can rewrite this equation in the form

d/dt(µ(t)y)=b(t)µ(t)y^n. Find the general solution of this equation by finding an appropriate integrating factor. Hint: Divide both sides of the equation

by an appropriate function of y.

I have problems solving this question. because this question is located in section (1.9) of the book which talks about exact equations and my problem is that

I cannot turn "d/dt(µ(t)y)=b(t)µ(t)y^n" to an exact equation form. I'd appreciate any help. :)

I found below question in a book by Martin Braun "Differential Equations and Their Applications An Introduction to Applied Mathematics (Fourth Edition)"

The question :

The Bernoulli differential equation is (dy/dt)+a(t)y=b(t)y^n. Multiplying through by µ(t)=exp(Integral of a(t).dt), we can rewrite this equation in the form

d/dt(µ(t)y)=b(t)µ(t)y^n. Find the general solution of this equation by finding an appropriate integrating factor. Hint: Divide both sides of the equation

by an appropriate function of y.

I have problems solving this question. because this question is located in section (1.9) of the book which talks about exact equations and my problem is that

I cannot turn "d/dt(µ(t)y)=b(t)µ(t)y^n" to an exact equation form. I'd appreciate any help. :)