1. Ordinary Differential Equations
Clicker questions

2. What is the order of the following differential equation
What is the order of the following differential equation? y’’ – 2 y’ + y = 0 1 2 3 4
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3. Is the following differential equation linear? y’’ – 2 y’ + y = 0
Yes No
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4. Are y1(x)=ex and y2(x)=x ex solutions of the following differential equation? y’’ – 2 y’ + y = 0
Yes No
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5. Are y1(x)=ex and y2(x)=x ex linearly independent?
Yes No
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6. Does the following initial value problem have a unique solution near x = 0, y = 1, y’=0? y’’ – 2 y’ + y = 0, y(0) = 1, y’(0) = 0
Yes No
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7. Does the following initial value problem have a unique solution near x = 0, y = 1, y’=0? y’’ – 2 y’ + y = 0, y(0) = 1, y’(0) = 0, y’’(0) = 2
Yes No
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8. Does the following initial value problem have a unique solution for all values of y0? y’ = y1/2, y(0) = y0
Yes No
Don’t know
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9. Does the following initial value problem have a unique solution near x =1, y = 1? y’ = y2, y(1) = 1
Yes No
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10. Does the solution to the following initial value problem exist for all values of x? y’ = y2, y(1) = 1
Yes No
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11. Does the following initial value problem have a unique solution for all values of x? y’’ – 2 y’ + y = 3 x, y(0) = 1, y’(0) = 0
Yes No 10
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12. Does the following initial value problem have a unique solution on the interval [-1, 1]? y(4) – x3 y’’ + 3 y = 0, y(0) = 1, y’(0) = 1, y’’(0) = 0, y(3) (0) = 0
Yes No 10
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13. Are y1(x)=x, y2(x)=x ex, y3(x)=x3 and y4(x)=x e3x linearly independent?
Yes No 10
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