(D^3-12D+16)y=(e^x+e^-2x)^2 #HigherOrderLinearDifferentialEquation L787

#complementaryfunction #particularintegral #chinnaiahkalpana #mathspulse Hello, people! Here is a video of finding solution to a given non-homogeneous equation f(D)y=Q from higher order linear differential equation, where Q=e^ax is an exponential function('a' being a real number). Please watch the video till end with patience. My hearty thanks to all the subscribers, supporters, viewers and well-wishers❤ With Love, Chinnaiah Kalpana🍁 Note: Order of a differential equation: A differential equation is said to be of order n, if the nth derivative is the highest derivative in that equation. Degree of a differential equation: The highest power of the highest derivative. Working rule to find particular integral: If Q=e^ax , where a is a constant. Then, P.I. = [ 1/f(D) ]e^ax , replace D=a (if f(a)≠0 ). = [1/f(a)]e^ax , since f(a)≠0. ******If f(a)=0 then it is possible only when a is the root of f(m)=0. When f(a)=0 then proceed the P.I. as follows P.I. = x [1/f'(D)]e^ax, f'(a)≠0 = x [1/f'(a)]e^ax Suppose that f'(a)=0 (where a is the root of twice for f(m)=0) then particuar integral becomes P.I. = x.x [1/f''(D)]e^ax, f''(a)≠0 =x^2[1/f''(a)]e^ax Suppose that f''(a)=0 (where a is the root of thrice for the f(m)=0) then the particular integral becomes P.I. = x^2. x [ 1/f'''(D) ]e^ax, f'''(a)≠0 =x^3 [ 1/f'''(a) ]e^ax and so on. For more such videos👇    • Higher Order Linear Differential Equations   You can also follow me on insta😊👍   / mathspulse_chinnaiahkalpana   Stay tuned to 'Maths Pulse'. Get rid of 'Maths Phobia'. Have a happy learning👍 #bscmaths #engineeringmaths #particularintegralsproblems #complementaryfunctionandparticularintegralproblems #particularintegralexamples