12.1 Consider the nonlinear first-order equation x = 2√x - 1. (a) By separating solution x₁(1). (b) Your solution should contain one constant of integration k, so you might reasonably expect it to be the general solution. Show, however, that there is another solution, x₂() = 1, that is not of the form of x₁ (1) whatever the value of k. (c) Show that although x₁(t) and x₂(t) are solutions, neither Ax₁(1), nor Bx₂(1), nor x₁(1) + x₂(t) are solutions. (That is, the superposition principle does not apply to this equation.)

12.1 Consider the nonlinear first-order equation x = 2√x - 1. (a) By separating solution x₁(1). (b) Your solution should contain one constant of integration k, so you might reasonably expect it to be the general solution. Show, however, that there is another solution, x₂() = 1, that is not of the form of x₁ (1) whatever the value of k. (c) Show that although x₁(t) and x₂(t) are solutions, neither Ax₁(1), nor Bx₂(1), nor x₁(1) + x₂(t) are solutions. (That is, the superposition principle does not apply to this equation.)