# Differential Equations

### Example 1

Solve the initial value problem.

*y*' = 4*x*^{3}, *y*(2) = 20

### Example 2

Solve the initial value problem.

*y*' = -sin *x*, *y*(0) = 2

### Example 3

Solve the initial value problem.

*y*' = *x*^{2} + *x*^{3} + 2, *y*(1) = 3

### Example 4

Solve the initial value problem.

*y*" = 4*x*, *y*(0) = 7, *y*'(0) = 5

### Example 5

Solve the initial value problem.

*y*' = -*e*^{x}, *y*(0) = -3