Bernoulli's Equation

The equation of the form dy/dx + Py = Qyn
where P and Q are constants or functions of x can be reduced to the linear form on dividing by yn and substituting 1/yn-1 = z

On dividing both sides by yn,
(1/yn)(dy/dx) + (1/yn-1)P = Q.

Put 1/yn-1 = z,
so that [(1-n)/yn]dy/dx = dz/dx
(1/(1-n))dz/dx + Pz = Q

dz/dx + P(1-n)z = Q(1-n)

Which is a linear equation and can be solved easily by the method discussed in the previous post.



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