# sample_problems1 - Name: UCLA ID: Please circle your...

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Name:UCLA ID:Please circle your section:Yin/Tuesday (3A)Marshak/Tuesday (3C)Baron/Tuesday (3E)Yin/Thursday (3B)Marshak/Thursday (3D)Baron/Thursday (3F)Instructions:1.Solve all problems completely. Give complete reasoning unless it is statedthat you donât need to.2.Show all your work. Partial credit will be given where it is possible tosee that you have a partial answer.3. No calculators are allowed, or necessary.4.No notes or references (including but not limited to the textbook) areallowed.5. You must answer the questions entirely yourself.6.If you need more space to work, please continue each problem on the backof the same sheet.7.Look at all the problems before starting!You may find that some seemeasier, or parts of them; do those first.The actual exam will have 5 questionsQuestionPointsScore112212312412512612Total:72
Math 3A (Ryan Reich) Midterm 1Page 1 of 71. (12 points)Mark each statement as âtrueâ or âfalseâ; one point each, and work will notbe taken into account.TFEvery separable differential equation is linear.The differential equation 4x(1 + 2y2)y0+ 5y= 0 is separable.
The differential equation 4x(1 + 2y2)y0+ 5y= 0 has an integrating factor
u(x).The differential equation 4x(1 + 2y2)dy+ 5y dx= 0 is exact.
Any differential equation in normal formy0=f(x, y) can be put in differential
formP(x, y)dx+Q(x, y)dy, and any equation in differential form can be putin normal form.

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