How do I know if I am using the right particular integral when solving a differential equation

Particular integrals will generally be derived in two different ways, depending on the type of the differential equation that you are solving. For example if it was a linear first order ODE, then you would have to solve e^(integral P.dx). Or, if you had a second order linear ODE, then you have have to guess the answer, (depending on the forcing function in the inhomogenous case), substitute the guess and its higher order derivatives into the ODE and solve for the unkown co-efficicient(s). The question becomes (" is this the right one " ) and the best way to find out is simply through an example. If your particular integral already appears in the complementary function you have just derived, then determining the unknown co-efficient will be impossible as it will lead to solving an inconsistent set of equations. in that scenario you would have to multiply by x (or even by x2 if that appears again). In the case of a first order ODE. The particular integral should be chosen such that the ODE simplifies into a derivative of a product of y and the integrating factor. Getting the right one only comes through practice and experience.

Answered by Vaikkun V. Maths tutor

9325 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the integral of y= e^3x / 1+e^x using calculus.


Show that the cubic function f(x) = x^3 - 7x - 6 has a root x = -1 and hence factorise it fully.


let y=6x^-0.5+2x+1, find dy/dx.


The equation of curve C is 3x^2 + xy + y^2 - 4x - 6y + 7 = 0. Use implicit differentiation to find dy/dx in terms of x and y.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences