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# Initial Value Problems Exercises

### Example 1

Determine if the function y = 4e -x is a solution to the IVP

y" + y ' = 0 and y(0) = 4.

### Example 2

Determine if the function f (x) = x3 is a solution to the IVP

3f (x) = xf '(x) and f (0) = 2.

### Example 3

Determine if the function y = x + 2 is a solution to the IVP

### Example 4

Determine if the function f (x) = sin x is a solution to the IVP

f (3)(x) = -f '(x) and f (0) = 0.

### Example 5

Determine if the function y = x2 + 4x is a solution to the IVP

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