AS/A2 Pure 5 Pure 6

P4 Topic 6: Second Order Differential Equations
The failure case
Second order differential equations of this form:.
have solutions with two parts: the complementary function and the particular integral. The type of particular integral depends on the nature of f(x). The following display shows examples where f(x) is an exponential function and we have a rare instance of the failure case. This means that the trial solution y = leqx is actually part of the complementary function.

Summary When f(x) = peqx, the trial solution is y = leqx. Note that if the trial solution is actually part of the complementary function, this is known as the failure case and the trial solution should be changed to y = lxeqx. This page uses HotEqn.