فيه حاجة اسمها I/O differential EQ

[darkknight]

سلام عليكم
فيه حاجة اسمها I/O differential eq فيها P , P^4 , P^3 ........ديه علينا ولا ايه؟؟؟؟؟؟؟؟؟:nar:

[darkknight]

ايه يا جدعان ... هو انا جى من المريخ؟؟؟؟؟؟
هو مش ده سيستيم برضو؟؟؟؟؟

[Esraa_62]

أيوه علينا يا بشمهندس دى حتى جت فى الميدتيرم

[Osama El3antably]

الـ P ده هوا الـ Differential Operator الي كنا خدناه في الرياضة السنة اللي فاتت ..
كنا بنسميه D ..
اللي هوا ..
X" = D(square)X

[Emily]

I/O equations
in a problem input and output are mentioned like fa input and x1 is an output so all you have to do is to get an expression for any other variable like may be x2 in terms of x1,it's derivatives and fa
so if input is u and the output is y you find I/O equation that contains u and y and their derivatives only and eliminate any other variable
so you can use the operator p to eliminate a variable
e.g.
y' +2y+2x=3u
2y'+5y-3y1'+2y1=0
(p+2)y+y1=3u
(2p+5)y+(-2p+2)y1=0
y1=(6p+15)/(2p^2+4p+1)*u
(2p^2+4p+1)y1=(6p+15)u
final answer
2y1"+4y1'+y2=6u'+15u
so you simply in stead of trying to find an expression for a difficult equation you transfer it to an algebraic equation
y''======>p^2
y'===========>p
y===========1
and so on