 In the integral solutions, λ and ε are dummy variables of integration (the continuum analogues of indices in summation), and the notation ∫"x""F"("λ") "dλ" just means to integrate "F"("λ") with respect to "λ", then "after" the integration substitute "λ" = "x", without adding constants (explicitly stated).When all other methods for solving an ODE fail, or in the cases where we have some intuition about what the solution to a DE might look like, it is sometimes possible to solve a DE simply by guessing the solution and validating it is correct.To use this method, we simply guess a solution to the differential equation, and then plug the solution into the differential equation to validate if it satisfies the equation.