DQ EXAM 1 9/21

Determine if each ODE is linear or nonlinear. If non linear, what term makes it non linear

linear

Determine if each ODE is linear or nonlinear. If non linear, what term makes it non linear

non linear

find general solution and solution to the initial value

how to idenifty linear and nonlinear

Tell yourself:

“If yy and its derivatives are separate and to the first power, it’s linear. If they’re multiplied, powered, divided, or inside a function, it’s nonlinear.”

If y, y′, y′′y,\ y',\ y'' are just standing alone with coefficients that depend only on xx, it is usually linear.

info slide (first-order linear equation)

info slide

existence and uniqueness theorem question

12834

5889.39

info slide

info slide

. Integrating Factor Flowchart

info slide , autonmous and non

info slide, 2nd ode homgenous

no no yes no

linear, -1, pi/2

non linear

not exact

a b c

no stable, semi x=13 . (the picture is showing info)

x=2 stable, x=4 unstable

dont forget to check 0

no

no

and also find general solctuion y(t) = …

and also find general solctuion y(t) = …

and also find general solctuion y(t) = …

(0,pi/2)

(-infinty,0)

and also find general solctuion y(t) = …

and also find partituclar solctuion y(t) = …

(0,3)

info slide

info slide

MAJOR INFO SLIDE

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amplitude, period, frequency

3m, pi s, 1/pi hz

amplitue, period,

u(t) have sqrt8 inseatd of 2sqrt2

just find the type of damp

4sqrt15