A-Level Further Maths I5-10 2nd Order Differential Equations: Particular Integrals Overview

[zanderbryant]

Hi, I’ve just seen another case where the particular integral contains a term from the complementary function. If one of the roots of the auxiliary equation is 0, the complementary function will contain a constant term, since e^0x is 1, so if your f(x) is a polynomial, you’d need to multiply your trial function by x to ensure there’s no constant term in it.

[zanderbryant]

Hi, really good video it helped me to understand this topic a lot better! Just one point, what if your complimentary function is in the form (A + Bx)e^px, because in that situation you have an Ae^px term and a Bxe^px term, so the trial function you showed wouldn’t work. I think you have to multiply the trial function by another x to get y = C x^2 e^px but just wanted to check with other people

[physicswithbalaj]

Hats off to you sir
You're one of those guys who're actually worthy of being called a "Sir" and a "Teacher"
Loads of love from someone not taking Further Math in Cambridge A Levels but still studying for fun :D

[hanson._.]

Hello, just wanna say that this is a really good vid that sums up the details of the possible f(x), one question, what would the trial function be when f(x) is some hyperbolic function like 5cosh (4x)? thank youuuu

[ELLIPTICALWR]

what comes after differential equations in further maths (in degree)?

[nosir]

Hi

When your differential equation is equal to Ax^2 + B, a quadratic function but without the x term, would our trial function still be a full quadratic, ax^2+bx+c to cover all eventualities?

[Joe-Fowler]

will there be a haloween special this year?