FOR REDUCTION OF ORDER
(D^2+4)y=sinx
@TuringTest :)) i have the answer but i dont know how it came with it :)

- anonymous

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- wasiqss

well i can tell you how to do it

- anonymous

that's great! can you help me? please? :)

- wasiqss

do you want complimentary or particular solution

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## More answers

- anonymous

both? and the general solution? :)))) please?

- wasiqss

y complimentary =d^2=-4
d=+2i, -2i
hence Y complimentary =C1 cos2x+C2 Sin2x

- wasiqss

Y particular = (Sinx)/(D^2 +4)
now the cofficient of x (that is with sin =1)
hence we put the square of the negative value of coffiecient of x in the variable D
hence it becomes
Sinx/(- (1^2)+4)
hence Y particular=Sinx/3

- anonymous

can you give me a detailed solution? like in integrating it? or what? does it need wronkian in reduction?

- wasiqss

Lol its the solution and detailed one and the general solution is Yparticular + Y general

- anonymous

so you mean the reduction of order is a simplier method compared to variation? or it depends?

- wasiqss

well i did the differential equations this way and i find it simple

- wasiqss

u in which grade

- anonymous

2nd year college

- wasiqss

im a first year college student though :D

- anonymous

hmm.. i thinkn you have k12 :)

- anonymous

so what's the steps that im going to put on my paper? :) first the yc then the yp immediately? and lastly the y?

- wasiqss

yehh exactly :)

- wasiqss

what is K12

- anonymous

woah. what a short process?

- wasiqss

yehh i will be glad to help u in these type of questions :)_

- anonymous

hence we put the square of the negative value of coffiecient of x in the variable D hence it becomes ??? wat do u mean of that? can u clarify it with me?

- wasiqss

like if its Sin 2x then the cofficient of x=2 and hence we would put the square that is 4 in this case and negative means i will add - to the square of the coffiecient .

- wasiqss

but remember we can only do that when it is D^2

- anonymous

so i shall only follow the process that you gave to me?

- wasiqss

yehh u should

- anonymous

Y particular = (Sinx)/(D^2 +4) now the cofficient of x (that is with sin =1) hence we put the square of the negative value of coffiecient of x in the variable D hence it becomes Sinx/(- (1^2)+4) hence Y particular=Sinx/3
so i will put this on my paper? lol

- anonymous

yp= sinx / (d^2+4)

- wasiqss

Yparticular = (Sinx)/(D^2 +4) now the cofficient of x (that is with sin =1) hence we put the square of the negative value of coffiecient of x in the variable D^2 hence it becomes Sinx/(- (1^2)+4) hence Y particular=Sinx/3

- wasiqss

now thats perfect

- anonymous

now the cofficient of x (that is with sin =1)???? this?

- wasiqss

yehh

- anonymous

wat do u mean? is it constant? sin =1?

- wasiqss

i mean if its sin3x then constant cofficient=3

- anonymous

ahh.. now i know! i get it. lol HAHA so if sin3x the it could sin3x/-3^2+4? i jst change 1 to 3

- wasiqss

yayyy finally u got it :)

- anonymous

hmm.. so the short process of yours will give me high score? :))

- wasiqss

yehhh :)

- anonymous

HAHA. thanks friend. i hope i can count on you next time :)

- wasiqss

Lol probability is low though :D

- anonymous

HAHA.. lol :)

- TuringTest

sorry, I need to review reduction of order...

- anonymous

hey turing test. i have a question. ahm. can wolfram able to answer laplace problems?

- amistre64

yes it can

- amistre64

http://www.wolframalpha.com/input/?i=laplace+inverse

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