second order

  1. J

    Finding the singular points for this differential equation

    Homework Statement If d^2/dx^2 + ln(x)y = 0[/B] Homework Equations included in attempt The Attempt at a Solution I was confused as to whether I include the power series for ln(x) in the solution. It makes comparing coefficients very nasty though. Whenever I expand for m=0 for the a0 I...
  2. S

    I Constructing a 2nd order homogenous DE given fundamental solution

    Homework Statement Given a set of fundamental solutions {ex*sinx*cosx, ex*cos(2x)} Homework Equations y''+p(x)y'+q(x)=0 det W(y1,y2) =Ce-∫p(x)dx The Attempt at a Solution I took the determinant of the matrix to get e2x[cos(2x)cosxsinx-2sin(2x)sinxcosx-cos(2x)sinxcosx-...
  3. faradayscat

    Differential equation with power series

    Homework Statement Solve y''+(cosx)y=0 with power series (centered at 0) Homework Equations y(x) = Σ anxn The Attempt at a Solution I would just like for someone to check my work: I first computed (cosx)y like this: (cosx)y = (1-x2/2!+x4/4!+ ...)*(a0+a1x+a2x2 +...)...
  4. kostoglotov

    Dynamic Damping in a simple spring system

    Homework Statement imgur link: http://i.imgur.com/Bv3qtPm.png Homework Equations The Attempt at a Solution From the FBD it is apparent that there is a constraint -k_1x_1 + k_2(x_2-x_1) + 5\cos{10t} = 0 If you combine this with {x}''_1 = -(k_1+k_2)x_1 + k_2x_2 + 5\cos{10t} and...
  5. kostoglotov

    Am I right?: solving u" = Au

    I know how to solve \frac{d\vec{u}}{dt} = A\vec{u}, I was just watching a lecture, and the lecturer related that solving that equation is pretty much a direct analogy to \vec{u} = e^{At}\vec{u}(0), in so far as all we need to do after that is understand exactly what it means to take the...
  6. S

    Engineering Initial and final values for second order circuits

    Homework Statement I am attempting to understand this example shown below: Homework Equations During stead state DC, the capacitor is an open circuit and the inductor is short circuited. The Attempt at a Solution [/B] The questions I have are really related to the concepts as I don't...
  7. VoteSaxon

    Confusing particular integral

    Homework Statement Well I am looking for the particular integral of: d2y/dt2 + 4y = 5sin2t The attempt at a solution As f(t) = 5sin2t, the particular integral yPI should look like: yPI = Acos2t + Bsin2t dyPI/dt = -2Asin2t + 2Bcos2t d2yPI/dt2 = -4Acos2t - 4Bsin2t Subbing in to the differential...
  8. kostoglotov

    Question concerning 2nd order homogeneous linear diff eqs

    Homework Statement Regarding the case where the auxillary (characteristic) equation has complex roots, we solve the quadratic in the usual way using i to get the general solution y(x) = e^{\alpha x}\left(C_1 \cos{\beta x} + i C_2 \sin{\beta x}\right) And the textbook shows y(x) = e^{\alpha...
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