{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

varconcoeff

# varconcoeff - x t = Ke at e at t Z e-aτ b τ dτ SOLUTION...

This preview shows pages 1–2. Sign up to view the full content.

THE CASE OF FIRST ORDER LINEAR CONSTANT COEFFICIENTS: the initial value problem. THE EQUATION: dx dt = a x + b ( t ) THE INITIAL CONDITION : x (0) = x o THE HOMOGENEOUS PROBLEM: dx dt = a x . SOLUTION OF HOMOGENEOUS PROBLEM: x h ( t ) = K e at . DIFFERENTIAL EQUATION FOR K ( t ) : K ( t ) = e - at b ( t ) . SOLUTION OF EQUATION FOR K : Any convenient solution will do, so we take the following one: K ( t ) = t 0 e - b ( τ ) 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
THE GENERAL SOLUTION:
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x ( t ) = Ke at + e at t Z e-aτ b ( τ ) dτ . SOLUTION OF THE INITIAL VALUE PROBLEM: Since x (0) = x o is the given initial condition and since x (0) = Ke + 0 = K , it follows that K = x o and the solution of the initial value problem is: x ( t ) = x o e at + e at t Z e-aτ b ( τ ) dτ . 2...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

varconcoeff - x t = Ke at e at t Z e-aτ b τ dτ SOLUTION...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online