# Calculus Course/Differential Equations/2nd Order Differential Equations

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## Contents

## 2nd Order Differential Equation[edit]

2nd Order Differential Equation is an equation that has the general form

## Characteristic Equation[edit]

2nd Order Differential Equations above can be rewritten as shown

Let

Then

- ) t

### Case 1[edit]

When

Then

Equation has *one real* roots

### Case 2[edit]

When

Then

Equation has *two real* roots

### Case 3[edit]

When

Then

Equation has *two compex* roots

## Special Case[edit]

### Case 1[edit]

Differential Equation of the form

Roots of equation

### Case 2[edit]

Differential Equation of the form

Roots of equation

## Summary[edit]

2nd Order Differential Equation

has roots depend on the value of

With