some calculus help for 12th math

[exotic lance]

find general solution of dy/dx+2y=sinx use tht integration factor method, also if there r ez methods to do pls tell

[exotic lance]

yo guys pls help

[bold glen]

!status

[near silo]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[bold glen]

alright so did u find integrating factor yet??

[exotic lance]

e^2x is IF

[bold glen]

so... its straight forward after that nah?

[exotic lance]

how to integrate sinx . e^2x . dx idk tht part tht 1 part keeps recurring

[bold glen]

oh

okay

so u need help with integration of that

[exotic lance]

tht 1 part of the equation keeps cming back and idk

[exotic lance]

yes

[bold glen]

alright lemme

[exotic lance]

this the actual question

[strange linden]

repeated integration by parts

then like terms

[exotic lance]

i am not getting tht

[bold glen]

try to get to this form
where I is ur original integral
I = f(x) + kI ...

[strange linden]

did you substitute dv = e^x

[exotic lance]

wait why substitution?

[strange linden]

integration by parts

v = e^x

u = sinx

du = cosx

then redo it

[exotic lance]

i am talking abt by integration factor method

[strange linden]

yes but didn't you get it while doing the method

[exotic lance]

is parts method ezier?

[strange linden]

no but you have to do it

[exotic lance]

i was checking the solution online but bro i didn't undersand anything there

[strange linden]

after you get muo(x)

like the one with e^2x

[strange linden]

yeah that's how you do it

[strange linden]

although dv = e^2x

[exotic lance]

bro i am not understanding this solution

[strange linden]

hence v = (e^2x)/2

[strange linden]

the solution looks unnecessarily complicated

[exotic lance]

exactly...

[strange linden]

they use too many substitutions

so what you do here

is just ibp

repeat it

here dv = e^2x

u = sinx

[exotic lance]

u can see in 2nd image tht sinx.e^2x will keep repeating after every integral

[strange linden]

yes and

if you get the integral of something along

e^2xsinx

js combine like terms

like you'll also get it on the l.h.s.

so the way you can find the integral is by

isolating it

then dividing by the multiple you get

[exotic lance]

hmm lemme try if i can do tht

[strange linden]

that's how you deal with this repetition

[bold glen]

u do integration by parts 2 times

and after doing it second time

u will see a term that is basically ur original integral / 4

take that to other side

like how we do algebra

I = f(x) + I/4 ... so the thingi remaining on right is ur answer ;p

[exotic lance]

so take common and cancel?

[bold glen]

yes

[bold glen]

its shown in this picture whaht im saying...

[exotic lance]

tht thng felt mad complex to follow thru

i am pretty sure i might forget a few steps during exam

is there a simpler way to do this?

[bold glen]

yea i just do D I method lol when have to deal with repeated

i dont think so.... i mean we could do taylor expansion but uk...

seems kinda overkill

idk

prolly will be more complex nvm

[exotic lance]

u mean taylor series?

i might lose marks for making a complex question more complex....

[bold glen]

yea

[bold glen]

yep

its overkill

• would be kinda monstrous task to put the answer back in term of cos and sin

[strange linden]

this would probably take too long

[exotic lance]

a 1 page answer became a book...

[bold glen]

yea i realised that

[exotic lance]

the whole 3hr exam i am sitting there and solving 1 question ;-;

[strange linden]

https://klipy.com/gifs/blackbeard-blackbeard-writing

[exotic lance]

so ye i think there is no other way than integration by parts

[bold glen]

we could do this by complex numbers lol

[exotic lance]

no need...

[bold glen]

u started ts

🥀

[exotic lance]

i don't want my method to hv i's in it...

[bold glen]

i was happy with my 2 integral by parts

[exotic lance]

simpler method using complex numbers...

[bold glen]

;-;

its like 4 lines lol

[exotic lance]

wait wht

how

[bold glen]

lemme do it on paint 2 mins

i dont know LaTeX

wait i think ull understand by just saying

okay so sinx is basically imaginary part of e^(ix) right

so e^2x * sin x will be imaginary part of e^(2+i)x

and its trivial integrating e^kx

we will get e^(2+i)x / (2+i)

[exotic lance]

this using euler's eqn?

[bold glen]

yes

e^ix = cos x + i sinx

one

[exotic lance]

hmm ok go ahead

[bold glen]

after that u get rid of 2+i in deno by multiplying by conjugate so e^(2+i)x * (2-i) / 5

after that convert exponent back into sin + i cos

and multiply by (2-i)

and the terms with i ... is ur answer

:p

[exotic lance]

shit thts actually ezier than parts method

[bold glen]

yea

its like 4-5 lines

on paper

[exotic lance]

ye i don't think i'll get makrs for it in exam tho

[bold glen]

too slow

[exotic lance]

i mean i could use tht to check my answer ngl

[bold glen]

ikr

great technique lol

[exotic lance]

fr thank you so much

[bold glen]

too late

[coral ridge]

Can you help ke with my problem instead

[bold glen]

when?

[exotic lance]

its been 36mins

[bold glen]

sure

i could try

:D

open new forum

[coral ridge]

Its already opened

Named geometry