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Practice Exam IMath 2410Name:Feb xth , 2019Exam One KeyInstructions: Answer each question to the best of your ability. Show your work or receive no credit. All answers must be written clearly. Be sure to erase or cross out any work that you do not wantgraded. Partial credit can not be awarded unless there is legible work to assess. If you require extra space for any answer, you may use the back sides of the exam pages. Pleaseindicate when you have done this so that I do not miss any of your work.Academic Integrity AgreementI certify that all work given in this examination is my own and that, to my knowledge, has not been usedby anyone besides myself to their personal advantage. Further, I assert that this examination was taken inaccordance with the academic integrity policies of the University of Connecticut.Signed:Exam OneKey(full name)Questions:Score:123145Total
1. (5 points) Solve the linear initial value problem(dy(x2 1) dx 2y (x 1)2y(2) 0Hint: Partial fractions may be helpful.Standardfinii5yfOyesyµ eSerpent IZa37aftyeS Iz doe fPcr LETferyIIolake3dFESLIT In3 ta TEc ZduGtc252t c3cZ17laellla II
2. (5 points) Consider the ODE(y 3 kxy 42x)dx (3xy 2 20x2 y 3 )dy 0,where k is to be determined.(a) Find k so that the given ODE is an exact equation.(b) Using this value of k, solve the given ODE.aMcnielNancyMy zy2 4KNy3zuy3tKuyt20My't Hey3y2y 40 my3 342 40 5gieseyXyzMeMy he eExact e3K sk coesbyfufy14long2k du tzxy2 zonZy3dyay cough3dg4k my 40dgzou'dff my3 skyxy3csnj4hckli.ggo hcun2fciecysuy3cSse2y4n24c3m2 gey
3. (5 points) Consider the ODE(xk yey/x )dxxey/x dy 0,where k is to be determined.(a) Find k so that the given ODE is a homogeneous equation.(b) Using this value of k, solve the given ODE.AMcncylmatetopMckoyNcte EySo boomyeCKakTheseetreeifb else y nunn't y eE ft'mEyeK 1yethese.glE Idysedatududa seed dyru3o 211NascudGet une Idasie duscan tunefdsenenonse ete ducanecase4dadye eebe tceout uda lHaeoo
4. (5 points) Consider the Bernoulli equationy0y yp ,where 0 p 1 is arbitrary.(a) Solve the given equation with p left arbitrary. The solution will depend on p.(b) Let yp denote your answer in part (a). Computelim ypp!0and compare the limit to the solution to y 0y 1.(c) (If you have too much time on your hands) What happens as p ! 1? One should expect the limitis the solution to y 0 y y. . . But the limit isn’t even well-defined for all x. . .at theeak the substitutionshouldbeidateEp udataeaggEpy ydefyadu C PJaeUi pCIPcufanipl pfa p EPC Ity yIµcceles dkeP Isnad PMcel PPkedadpinuyplutoµf dueuI t cebµpEieu PuLineaEgcuyCyi tceloffuf d EhIeon5Actually well elefenednessdependsef e du iceuand ceit cese
5. (5 points) Consider the IVP(y0 x y2y(0) 0.Let y be a solution to this IVP, and use Euler’s method with step h 0.1 to approximate y(0.3). Indicateclearly all relevant xk , yk , f (xk , yk ). Round your final answer to 3 decimal places.hykYseco lonooforay httf o.o o to iNothfox oo l ofcn.gs sexyOo Io l toCo 1 0210.1 too.o io ItoiYf ozUzo z t o IYyoo Zo oh ol t o.o lO o soo Io 31o sI Iy cuz yoI o03001oo6
Math 2410 Practice Exam I Feb xth, 2019 Name: Instructions: Answer each question to the best of your ability. Show your work or receive no credit. All answers must be written clearly. Be sure to erase or cross out any work that you do not want graded. Partial credit can not be awarded unless there is legible work to assess. If you require extra space for any answer, you may use the .
