hw 9 - KATHERINE HUANG-OUYANG Assignment 9 due at 06:00am...

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KATHERINE HUANG-OUYANGMath-1B-Lect-2-Fa13Assignment 9 due 11/06/2013 at 06:00am PST1.(2 pts) LetAandkbe positive constants.Which of the given functions is a solution todydt=k(y+A)?(2 pts) Find a positive value ofkfor whichy=cos(kt)satisfiesd2ydt2+y=0.A.y=A-1+CeAktB.y=-A+CektC.y=A+Ce-ktD.y=A-1+Ce-AktE.y=-A+Ce-ktF.y=A+CektSOLUTION:SOLUTIONWe can find the correct answer by plugging the answers intothe differential equation to see which satisfies the equation.Here,ddt(-A+Cekt) =kCekt, so that, plugging in, we havekCekt=k(-A+Cekt)-A,a true statement, so that the correct answer isy=-A+Cekt.
Answer(s) submitted:B(correct)Correct Answers:B2.(2 pts) Find the value ofkfor which the constant functionx(t) =kis a solution of the differential equation 2t5dxdt-6x+3.60555127546399, -3.60555127546399, 06.(2 pts) Verify that every member of the family of func-tionsy=lnx+Cxis a solution of the differential equationx2y0+xy=1.Answer the following questions.9=0.Answer(s) submitted:9/6(correct)
3.(2 pts) For what values ofrdoes the functiony=erxsat-isfy the differential equationy00-7y0+12y=0?Find a solution of the differential equation that satisfiesthe initial conditiony(10) =1.
4.(2 pts) Find a positive value ofkfor whichy=cos(kt)satisfiesd2ydt2+y=0.
5.(2 pts) Find all values ofkfor which the functiony=sin(kt)satisfies the differential equationy00+13y=0. Separateyour answers by commas.Answer(s) submitted:sqrt(13), -sqrt(13), 0(correct)Correct Answers:3.60555127546399, -3.60555127546399, 06.(2 pts) Verify that every member of the family of func-tionsy=lnx+Cxis a solution of the differential equationx2y0+xy=1.Answer the following questions.1.Find a solution of the differential equation that satisfiesthe initial conditiony(1) =10.
2.Find a solution of the differential equation that satisfiesthe initial conditiony(10) =1.
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8.(3 pts) The solution of a certain differential equation is ofthe formy(t) =aexp(1t)+bexp(3t),whereaandbare constants.The solution has initial conditionsy(0) =3 andy0(0) =5.Find the solution by using the initial conditions to get linearequations foraandb.

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