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# Differential Equations

# Initial Value Problems Exercises

### Example 1

Determine if the function *y* = 4*e*^{ - x} is a solution to the IVP

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

### Example 2

Determine if the function *f* (*x*) = *x*^{3} is a solution to the IVP

3*f* (*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* = *x*^{2} + 4*x* is a solution to the IVP