Some First-Order Nonlinear Differential Equations

Certain nonlinear first-order differential equations can be reduced to linear equations by an appropriate change of variables [1, 2]. For example, it is always possible for the James (Jacob) Bernoulli’s (1654–1705) equation \(y'+p(t)y~=~q(t)y^n,~~~n\ne 0,~1.\) In (2.1), \(n=0\) and 1 are excluded because in these cases the Eq. (2.1) is obviously linear.