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test2_Solution

# test2_Solution - 2 Math 242 Spring 2OtL Test Nane.9.L(ft.4...

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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 -J)=\ \A+ A +S = o ) E4 = -S' *= - l, I = -2' = (,Y (*f + \$f rqr + 6A13s ) \,, - -;lnlx-?wL'x 6" Lr l\$*+(At\$) xt6At5&-p*-ka*s)x-?a-;16*yr{*Qnt8)x .b-.6-u' = kxex l=e t ( 6* +gg-2/A -L6+e) - 4 r -24 = -2 s''= 0lt*)r* &''pN x(Gptg - qA -B +al* g) \hn=q r A=\ \h*zo=c b= eoh4','^ Jc() --YC t J6, t gst C, ex + crsin x t Cstdi,x - si n fu - gresex a ft?-z*)€x

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