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

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

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

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

Algebraic!
 2 years ago
Best 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 ?

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

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

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

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

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

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

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

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

Algebraic!
 2 years ago
Best ResponseYou've already chosen the best response.1look 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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Algebraic!
 2 years ago
Best ResponseYou've already chosen the best response.12a*cos^2(x)  2a*sin^2(x) +4a cos^2(x) = 4sin^2(x)

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

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

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

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

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

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

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

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

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

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

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

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

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