Explore BrainMass

Explore BrainMass

    Solve a 2nd order ODE.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Use methods of undetermined coefficients to find one solution of:

    y'' + 2y' +2y =
    (10t+7)e^(-t)cos(t)+(11t+25)e^(-t)sin(t)

    © BrainMass Inc. brainmass.com February 24, 2021, 2:32 pm ad1c9bdddf
    https://brainmass.com/math/ordinary-differential-equations/solve-2nd-order-ode-27369

    Solution Preview

    First the homogenous solution. The charac. equation is r^2+2r+2=0 which gives us:
    r= -1+i and r= -1-i, then yh= c1exp(-t)cos(t)+ c2exp(-t)sin(t).

    Now in this case the guess for the particular solution is yp= (at+b)exp(-t)cos(t)+ ...

    Solution Summary

    A 2nd order ODE is solved. The solution is detailed.

    $2.19

    ADVERTISEMENT