## Math Problem Statement

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Ordinary Differential Equations (ODE)

Reduction of Order

Initial Value Problems

Linear Independence

### Formulas

-5t² y'' + 4t y' + 2y = 0 (Given ODE)

Reduction of Order Assumption: y₂(t) = v(t) y₁(t)

Wronskian to check linear independence

### Theorems

Reduction of Order Theorem

Linearly Independent Solutions Theorem

### Suitable Grade Level

College Level - Advanced Calculus or Differential Equations

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