Solving Differential Equations

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Objectives 1a-1c Information

Thomas Smrtにより

How To Solve A Differential Equation

Tyler Knudsonにより

Chemical Reaction l

Elizabeth Topferにより

Differential Equation

Michael Lopezにより

You will have to use Euler's Method to approximate a solution

Yes, seperate and solve directly

Use the form Y=C1e^r1t+C2e^r2t

Is it a 1st order?

You could try converting in to a system of first order DE's, put in to a martrix, and solve using Eigenvectors

Real independent roots

Use the form Y=C1e^rt+C2te^rt

Than you must take the Laplace transformation, solve for L(y), then take inverse Laplace. NOTE- you will not be able to entirely solve without initial conditions.

First find the homogeneous solution

No, above 1st order

Is it homogeneous?

yes

First find the homogeneous solution using the method below, then come back here.

Does it include a step function?

Imaginary roots

Use the form y=e^at(C1costbt+C2sinbt)

Integrating Factor

Then you must use Variation of parameters

Find p(t), muliply both sides by u(t), carry out integration, then solve for y.

Form the characteristic equation with powers of r that match orders of y as well as matching all constant coefficients. Then proceed to factoring.

Take the Laplace transformation, solve for L(y), and take inverse Laplace, NOTE- You need initial conditions to solve completely.

Now, use Undetermined Coefficients to solve for particular solution

NO

Can you put it in standard form?

No? You missed something, turn around.

BEWARE- SERPENTS HAVE BEEN SPOTTED IN THIS AREA!

Is forcing function a "black sheep"?

Real, repeated roots

Is it seperable?

Yes

No

Is it a Bernoulli equation?

With some manipulation, you can use Integrating Factor

Basic techniques for solving Ordinary Differential Equations

Is differential equation Linear?