Thread: 2nd order diff eq.

Ok. One more question.

Consider the equation d^2y/dt^2 + B(dy/dt) + 2y = 0. Where B is a real parameter. Find all values of B such that the solutions except the trivial one Y(t)=0, are oscillatory. And find all the values of B that are growing oscillations.

I switched the equation to r^2 + Br + 2 = 0 and used the quadratic formula to get r = B/2 + or - {square root of (B^2 - 8)] / 2 i now I'm not sure where to go from here to find the values that are oscillatory.

Any help would be appreciated. Thanks.

Originally Posted by billbarber

Ok. One more question.

Consider the equation d^2y/dt^2 + B(dy/dt) + 2y = 0. Where B is a real parameter. Find all values of B such that the solutions except the trivial one Y(t)=0, are oscillatory. And find all the values of B that are growing oscillations.

I switched the equation to r^2 + Br + 2 = 0 and used the quadratic formula to get r = B/2 + or - {square root of (B^2 - 8)] / 2 i now I'm not sure where to go from here to find the values that are oscillatory.

Any help would be appreciated. Thanks.

Oscillatory solutions if the discriminant of the auxillary equation is less than zero. Review your classnotes or textbook.

got it. thanks.