(D^3+1)y=(e^x+1)^2

[@MathsPulseChinnaiahKalpana]

If Q = e^ax, where a is a constant
then,
P.I. = [1/f(D)]e^ax , replace D=a
= [1/f(a)]e^ax , provided f(a)≠0.
If f(a)=0 then it is possible only when a is the root of the auxiliary equation.
When f(a)=0 then proceed the P.I. as follows
P.I. = x [1/f'(D)] e^ax
= x[ 1/f'(a)] e^ax, provided f'(a)≠0.
Suppose that f'(a)=0 (where a is the root of twice for the auxiliary equation) then the particular integral becomes,
P.I. = x^2 [1/f''(D)] e^ax
= x^2 [1/f''(a)] e^ax, provided f''(a)≠0.
Suppose f''(a)=0 (where a is the root of thrice for the auxiiary equation)then the particular integral becomes,
P.I. = x^3 [1/f'''(D)] e^ax
=x^3 [1/f'''(a)] e^ax , provided f'''(a)≠0 and so on.

[@pramod5240]

Thanks a lot for this video 👍

[@nithishlingam6269]

Very well explained mam 👌

[@Sindhuuu99]

This vedio deserves more likes ❤❤❤

[@mukeshkumarsainikarnasaini8644]

Thanks ma'am

[@akainth01]

Omg....... What a great method 😍

[@OpOp-ck2dt]

Mam can u make video on standard form 1 2 3 4 in m2

[@pradeepnayak9515]

Akka m chepthunnavo emo oka mukka artham kaledhu