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Sourav posted an Question
July 22, 2020 • 04:16 am 30 points
  • IIT JAM
  • Mathematics (MA)

If general solution of the differential equation ay+ by +cy +dy=0 is linearly spanned by e", sin x and cos x, then which one of the following holds? (a) atb-c-

If general solution of the differential equation ay+ by +cy +dy=0 is linearly spanned by e", Sin x and cos X, then which one of the following holds? (a) atb-c- d= 0 (6) a +b+c+d=0 (c) a - b +c-d=0 (d) a-b-c- d= 0 34.

3 Answer(s) Answer Now
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  • Shashi ranjan sinha best-answer

    see the attachment. first option is also satisfied with the values of a,b,c,d....so it is also correct

    cropped7914135974820089827.jpg
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    okay but please see this . is it wrong?

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    your reply is very helpfult for me

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    ur whole explanation is correct.... just mention a thing that since it is 3rd order differential equation, therefore a is not equal to zero and so we can divide other coefficients by a .....

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    sorry I wrote a mistake in previous reply, that's why I deleted it...

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    If you're satisfied with my answer, plz accept the answer.

  • Kiran goswami

    in this question solutions is the linear span by e^x,sinx and cosx. and diff. eq. is homogeneous so they satisfied the eq., when we put e^x in the equation we get options b, but when we put sinx and cosx we doesn't get any option.

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    but I get option a & b

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    how you get option a plese give explanation.

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    see please

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    is it wrong?

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    but you don't know that a is 0 or not than how you divide by a. only one process is put all the solutions in eq. and get the option.

  • comment-profile-img>
    Sourav Jana

    but I think ans is a & b

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    but I see that given ans is b

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    in question , there is written which one of following is correct this imply only one is correct

  • comment-profile-img>
    Deepak singh 1 best-answer

    proof of option b , a is also correct

    cropped104537140.jpg
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    option b is true

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    any doubt please ask

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    just find auxiliary equation and put D=1 in auxiliary equation as e^x is solution

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    this pic is more clear..

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    I think there is misprint in option a

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