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lilMissMindset
Group Title
DIFFERENTIAL EQUATION:
help please, anybody.
(D^2 +4)y =4sin^2 (x)
 2 years ago
 2 years ago
lilMissMindset Group Title
DIFFERENTIAL EQUATION: help please, anybody. (D^2 +4)y =4sin^2 (x)
 2 years ago
 2 years ago

This Question is Closed

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
y= a cos2x ?
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
guess that substn should work..
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
aaa. i think i got it. wait, i'll try.
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
ohh wait,,i didnt see a "y" also in there. !!
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
@shubhamsrg I think it's just written in 'operator' notation... \[\frac{ d^2y }{dt^2 } +4y = 4\sin^2x\] correct @lilMissMindset ?
 2 years ago

shubhamsrg Group TitleBest ResponseYou've already chosen the best response.0
there's a y also with D^2 .. i had got that,,i didnt see a y being multiplied to whole that time..sorry..
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
\[\frac{ d^2y }{ dx^2 } +4y =4\sin^2x\] rather.
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
yes, tat's it
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
that*
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
yes he's correct I believe y =a*cos^2 x
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
did you get it to work?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
that's the particular soln. anyway...
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
isn't it like, Acosx+Bsinx+Cxcosx+Dxsinx
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
since sinx is twice? applying case 4 of undetermined coefficients
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
where it has some repeated imaginary root
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
look d^2 (a*cos^2(x)) /dx^2 +4a cos^2(x) = 4sin^2(x) second derivative of a*cos^2(x) is 2a*cos^2(x)  2a*sin^2(x)
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
this is for the particular solution...
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
finding the homogeneous solution shouldn't be a problem...
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
\[\lambda ^2 +4 =0\]
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
lambda = 2i
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
i'll work on it. please guide me still, in case i get stuck.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
hold on... can you tell me what part is giving you problems?
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
getting Yp gives me a lot of trouble. since you told me that it's acos^2 x, i am differentiating it now.
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
how about if the given is cos^x, then Yp=asin^2 x?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
if the forcing term is cos^2 x you mean?
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
yes.
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
i forgot 2, lol.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
yeah, for the same equation, I believe that a*sin^2 x would be the trial solution then...
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
yes. it would. just checked it.
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
thanks!
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
darn, i can't do it. show me a brief solution please. so i can learn how.
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
just for the Yp part. swear.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
well, I did it already (a*cos^2(x))" +4a cos^2(x) = 4sin^2(x)
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
2a*cos^2(x)  2a*sin^2(x) +4a cos^2(x) = 4sin^2(x)
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
hmm, I see your point ...
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
I guess you'll be needing something like yp = a*cos^2(x) + b*sin^2(x)
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
let me try it out and see...
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
sure. :)
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
seems to work... I got a= 2 b=2
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
so 2cos^2 x 2sin^2 x
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
answer here in the book is 1/2(1xsin2x) for the Yp part.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
I'll assume that's (1/2)*( 1  x*sin^2 x )
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
yes.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
you should check the original, I think you might have written the problem wrong...
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
you left out and x I think...
 2 years ago

lilMissMindset Group TitleBest ResponseYou've already chosen the best response.0
i don't think so.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
(1/2)*( sin^2 x  x*sin 2x ) ??
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
I don't see how (1/2)(1xsin2x) can work... maybe I'm missing something.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
something's off in your original equation or that soln.
 2 years ago
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