(D^2+D+1)y=x^3 #HigherOrderLinearDifferentialEquation L843

#higherorderlineardifferentialequations #differentialequations Hello, Everyone! Here is a video of higher order linear differential equations problem, where Q is of x^k (or x^n) form. We will be solving P.I. using binomial series. Please do watch the video till end and keep learning happily. My heart thanks to all the subscribers, supporters, viewers and well-wishers❤ With Love, Chinnaiah Kalpana🌹 Note: When the RHS is x^n (or x^k), n is +ve integer: P.I = [1/f(D)]x^n Rewrite f(D) to (1+x) form P.I = [1/(1+x)] (x^n) = [(1+x)^(-1)] (x^n) i.e., [f(D)]^(-1) × x^(n) Here, using binomial series, expand (1+X)^(-1) in ascending powers of D upto the power of x, and simplify(upto D^n). [* If Q is x^k suppose if we have k=2 find D(Q) and D^2 (Q)=D(D(Q)) since D^k(Q)=0 for k=3,4,..] Formulae: 1. (1+x)^(-1)= 1-x+x^2-x^3+...∞ 2. (1-x)^(-1)= 1+x+x^2+....∞ 3. (1+x)^(-2)= 1-2x+3x^2-4x^3+....∞ 4. (1-x)^(-2)= 1+2x+3x^2+4x^3+....∞ For more such videos👇    • Higher Order Linear Differential Equations   You can follow me on instagram😊👍   / mathspulse_chinnaiahkalpana   Stay tuned to 'Maths Pulse'. Get rid of 'Maths Phobia'. Have a happy learning👍 #bscmaths #engineeringmaths #particularintegralsproblems #particuarintegralwithxpowern #particularintegralwithxpowerk #engineeringmathematics #problemsonparticularintegrals