1. Ordinary Differential Equations
Clicker questions

2. Is the following differential equation linear? y’’ – 2 y’ + y = 0
Yes No 10
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3. Are y1(x)=ex and y2(x)=x ex solutions of the following differential equation? y’’ – 2 y’ + y = 0
Yes No 10
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4. Are y1(x)=ex and y2(x)=x ex linearly independent?
Yes No 10
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5. Does the following initial value problem have a unique solution near x = 0? y’’ – 2 y’ + y = 0, y(0) = 1, y’(0) = 0
Yes No 10
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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, y’’(0) = 2
Yes No 10
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7. Cannot decide based on what’s given
Does the following initial value problem have a unique solution for all values of y0? The direction field is provided y’ = y1/2, y(0) = y0
Yes No
Cannot decide based on what’s given 10
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8. 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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9. Which of the following is a particular solution of ?
y1=
y2=
y3=
y4=
:10

10. 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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