MATH 2214 Midterm: MATH 2214 Virginia Tech 3.9 Exam
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2 = 1. u1 = ln cos t, u2 = t. yp = cos t ln cos t + t sin t: we look for a particular solution of the form yp = u1(t)et + u2(t)t2et. 3: we look for a particular solution of the form yp = u1(t) sin t + u2(t)t sin t. 2(sin t + t cos t) = t sin t. u . 6 sin t: to follow the solution given here, you need to know that d dt z t. 0 f (t, ) d = f (t, t) + z t. This is a special case of the chain rule for several variables. De ne and observe that h(x, t) = z x. 0 f (t, ) d , d dt h(t, t) = We now apply this with (t, ) d (cid:17)(cid:12)(cid:12)(cid:12)x=t f (t, ) = In this fashion, we nd y =
