Thread: Challenging Differential Equation (For you, it''s probably cake)

http://www.math.rutgers.edu/~songyun...examreview.pdf

Does anyone know how to do problem 10 here?

I got the rest, but this one is confusing and I don't know what to do.

You're homogeneous solution is x = Ae^(-t)cos(t) +Be^(-t)*sin(t)

How did you go about trying to find the particular solution?

If you use undetermined coefficients

xp = Cte^(-t)cos(t) +Dte^(-t)*sin(t) you have to multiply by t since

e^(-t)*sin(t) and e^(-t)*cos(t) are homogeneous solutions

If you use variation of parameters W = e^(-2*t)

you obtain z1' = -sin(t)^2 z2 ' = sin(t)cos(t)