Jump to content

Calculus Course/Differential Equations/2nd Order Differential Equations

From Wikibooks, open books for an open world

2nd Order Differential Equation

[edit | edit source]

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

Characteristic Equation

[edit | edit source]

2nd Order Differential Equations above can be rewritten as shown

Let

Then

) t

Case 1

[edit | edit source]

When

Then

Equation has one real roots

Case 2

[edit | edit source]

When

Then

Equation has two real roots

Case 3

[edit | edit source]

When

Then

Equation has two compex roots

Special Case

[edit | edit source]

Case 1

[edit | edit source]

Differential Equation of the form

Roots of equation

Case 2

[edit | edit source]

Differential Equation of the form

Roots of equation

Summary

[edit | edit source]

2nd Order Differential Equation

has roots depend on the value of

With