## Math Problem Statement

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Differential Equations

Initial Value Problems

Integration

### Formulas

y^(4)(t) = -sin(t) + cos(t)

y^(3)(t) = ∫(-sin(t) + cos(t)) dt

y''(t) = ∫(cos(t) + sin(t)) dt

y'(t) = ∫(sin(t) - cos(t)) dt

y(t) = ∫(-cos(t) - sin(t) + t + 1) dt

### Theorems

Fundamental Theorem of Calculus

Initial Value Theorem for Differential Equations

### Suitable Grade Level

College Level (Calculus II/III, Differential Equations)

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