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MTH 205-Test 2-Solution

# MTH 205-Test 2-Solution - 1(8 points Find the general...

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Unformatted text preview: 1.(8 points) Find the general solution of the following differential equation: 3;”) — 4g“) + 4y“ — 16y” _—. 0 “‘d-“mh‘w’t ism’L: Q m4 (m...4_\ *4”). (h “dale wi‘ {wimp} Q,“ “Q 2Q 2.(10 points) Solve the following Initial Value Problem: y= E. W) =0, y’(1) =0. 3.(8 points) Use the method of undetermined coefﬁcients to ﬁnd the general solution of the non-homogeneous differential equation: y” + 3y' + 23; = 8-3 L h‘ *3“* 2— '29 =7 (MJerQ‘M-ﬁ =0 418 points) Find the general solution of the following differential equation: my“) _ ym = 0 x+iéﬁﬂ Kant.“ : Q m(m"ﬁ(M—L)Chn-—“6‘) -—~n(rn-—I\ (In—Zn : Q QO—tMm-o.) (On-.3).— q —.-. o h" (“Hum-Q 0" ~ﬂ 1:: “'1 H \‘leh:\}m51Lqml—;ﬂ 5.(6 points) Let y1 = Sin 3x be a solution of the differential equation 1;" + 9y 2 {I Find a second linearly independent solution 342 for the differential equation using reduction of order. '82- '22“ ﬁrian I . ‘3: —_ u {punsx + 7aMCT‘q‘h‘5K u H - ‘ ' L3; __ u ‘émsk arouseg 5); +5“ Cogs 3x -—°\U‘§ih3x one = *4" EM“ * 6L“ We“ “monk H 32“" ai‘hL ‘5'— ca Hug ‘ a _ . . lhstcém Poissx -°\ D\\‘\hgx «yakhgx :_ Q l . dcgj‘hsk +€"‘I 0*?» ex -= Q 1"“ “4:141 6.(10 points) A 4-foot spring measures _8__feet long after a mass weighing 8 lbs is attached tab—it. The Elaium through which the weight moves offers a ' resistance numerically equal to \/§ times the instantaneous velocity. Find the equation of motion if the weight is released from the mullibriumposition with a downward velocity of 5 ft/s. Find the time at which the weight attains its extreme diaplaoeiﬁent fro-me equilibrium position. Does the weight passes the equilibrium position, if it does, ﬁnd the ﬁrst time it passes through it. ®:«' 1 W :8 1F=ﬁ 5:L+ _ b=a “Na-3......l %' K-L 3L_; 7.(3 points) Let y1 = 32" and y2 be two linearly independent solutions of a. second-order differential equation such that W(yhy = —4. Find yg. ...
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