test2_Solution

test2_Solution - 2 Math 242, Spring 2OtL Test...

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Math 242, Spring 2OtL Test 2 Nane:.9.L(ft,?.4. .... 1. (30 points) Find the general solution (i.e., all solutions) of the nonhomogeneous differential equation: Y"' - y" * a' - g : 4:te' - 15sin2r. You may want to check your work by verifying that your answer satisfies the differential equation. D f 3- cat {-- I = C \ O <o{o,Jrn &t {"'- J"* ti- Y= -lGin"l .r? (,5--t)r (Gr) =o \ \ = A5i^]x + bwL,x q\"1!.9 \i =)gcos'-^$sinLx tr=\ )'.f -- tL | -\ w'.- I + ' -4Asinlx - ItbccsLx \ = C,{ - Crfrnx * %Co!K _l *il = - gA tos}* t x$ sinax ,ly+ [S -8A cesy*+ *&eifix + 4ftin )x+ 4(> rps?-x . t 1\ ^x,,)\ t^-z n.\ax I +r,Acss?x-etssi'"rx-'Asinlx-$g"'gfu=-t{<'tin) \ = (A^ trg)gt'Qti = (4f +6x\4x -l +dwcs'/-^ - ^'Q)l'''*'' '-- d = er [Af+ Ax +anx+e)-ex(4f.CI,n:q{1-s I,^(-JYYya 9r sinex(s6 !q!.?,-Atr{) = o \ *g)\ -\) c { =g*(+f. [zn$**Bt2ArtzAr,6)="'\ l^[A+3t>=c ]0.=?A _ ,,. ^\ nn,^0\ ll a6t3Attt=ol+s leh$+s;'c = (.y {4f +Q,+rc) * +2,A*zb) I I a6 r3A ttt=o l+s lehlA+s' s = er(*rt* Qhril\u*9,fup&+9$x+ 44
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This note was uploaded on 12/13/2011 for the course MATH 242 taught by Professor Staff during the Spring '11 term at South Carolina.

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test2_Solution - 2 Math 242, Spring 2OtL Test...

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