Non-autonomous scalar discontinuous ordinary differential equation (Q557000)

A scalar differential equation is considered. The right-hand side of the equation represents a sum of a discontinuous function \(f(x)\) and a function \(h(t)\). The functions \(f\) and \(h\) are nonnegative, \(f\) is finite a.e. and \(1/f\) and \(h\) are Lebesgue integrable. The existence of a local absolutely continuous solution is proved. The authors make a mistake asserting that the problem in example 6 has only two solutions. In fact, the problem has an uncountable set of solutions.