- #1

- 71

- 0

## Homework Statement

Find the general solution to

x'' -2x' + 5x = 0

## Homework Equations

Charasteristic polynomial.

Quadratic equation.

General solution form for complex roots.

## The Attempt at a Solution

form the char polynomial:

m^2 -2m +5 = 0

Solve for roots:

(-2 (+-)SQRT(2^2 - 4(1)(5)))/2

-1+SQRT(-16)

-1-SQRT(-16)

m1 = -1+4i

m2 = -1-4i

Insert into general solution form:

y = (e^ax)(Acoswx + Bsinwx)

y = (e^-1x)(Acos4ix + Bsin4ix)

**General solution: (?)**

y = (e^-x)(Acos4ix + Bsin4ix)

y = (e^-x)(Acos4ix + Bsin4ix)