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Snehasish Ghosh posted an Question
July 05, 2020 • 01:48 am 30 points
  • IIT JAM
  • Physics (PH)

Is the method of solving a cauchy-euler homogeneous linear differential equation the same as that of linear different equation with constant coefficients? i mea

Is the method of solving a Cauchy-Euler Homogeneous Linear differential equation the same as that of Linear different equation with constant coefficients? I mean can we find the solution of a Cauchy- Euler homogeneous linear differential equation by just finding the C.F and P.I. as we do in Linear Homogeneous Differential Equations with constant coefficients?

3 Answer(s) Answer Now
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  • comment-profile-img>
    Ujjawal vishal

    yes we have to find cf and pi... but in cauchy euler method ,we need different trick to solve it... we take x=e^z and then chnage derivative of y into derivative of z accordingly

  • comment-profile-img>
    Dhairya sharma

    we have to deal both in similar manner.....but for convenience and ease of calculation in homogeneous eqn we take like d^2 = D(D-1)

  • comment-profile-img>
    Chandra prakash best-answer

    yes dear

    eduncle-logo-app

    for convenience and ease of calculation in homogeneous eqn we take like d^2 = D(D-1)

  • comment-profile-img>
    Dhairya sharma Best Answer

    yes

    eduncle-logo-app

    we may take it

    eduncle-logo-app

    Ma'am, then what is the use of the method of variation of parameters?

    eduncle-logo-app

    I mean where should we use it?

    eduncle-logo-app

    it's for ease of solution.....like we can reduce calculation

    eduncle-logo-app

    like if that method is applied here then it's possible that we can stuck in calculation so

    eduncle-logo-app

    Ma'am, If I learn how to solve Linear Differential Equations with constant coefficients (Both Homogeneous and Non- Homogeneous), will I be able to solve Linear Differential Equations with variable coefficients by using the same process?

    eduncle-logo-app

    no....there will be another method but no need to do that

    eduncle-logo-app

    Ma'am,means?

    eduncle-logo-app

    i mean there would be an another method for that

    eduncle-logo-app

    Ma'am, please check my texts I sent you.

    eduncle-logo-app

    ok

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