Consider the differential equation ay" + by' + cy = g(x), where a, b, and c are constants. indicate for which input functions g(x) the method of undetermined coefficients (uc) is applicable and for which the method of variation of parameters (vp) is applicable. (some may be both.) (a) g(x)=e* in x (b) g(x) = sig (d) g(x) = xº cos x (e) g(x)=-2x pet 70 (c) g(x)=sin 2x (f) g(x) = sinx

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

gdp is the best phrase!