Key to Math 336 Old Test 2


1. 27.

2. See notes.

3. c_1 e^{-x/5} +c_2 +c_3 x +c_4 e^{3x/2} -3 x^2.

   c_1 cos(3x) +c_2 sin(3x) +c_3 x cos(3x) +c_4 x sin(3x).

   c_1 e^{-2x} +c_2 x e^{-2x} +c_3 e^{2x}.

4. (A x^2 +B x^3 +C x^4 +D x^5)
   +(E e^x cos x +F e^x sin x +G x e^x cos x +H x e^x sin x)
   +(I x e^{2x} +J x^2 e^{2x} +K x^3 e^{2x})

5. c_1 e^{3x} +c_2 x e^{3x} +e^{3x} /(12 x^3).

6. dv/dt =(400 -v^2) /100, ..., v(t) =(20 e^{2t/5} -20) /(1 +e^{2t/5}),
   v(10) appr. =19.28 (ft/s), v(infinity) =20 (ft/s).