Differential equations

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Differential equations

place in standard form.... See example.

1(X)'' +/-#(X)'+/-#(X)=somethng

Highest order X has a 1 in font of it.

Also make sure that the variables are seperated you may need to use seperation of variable.

Matrix

For matrix and some systems use eigenvectors and eigenvalues to solve. If it can be put into a matrix format than use this.

Second Order

Non-homogeneous

For non-homogeneous problems us the follow methods.

Variation of parameters

found in section 4.5

Undermined coefficients

This method is found in section 4.4

Homoheneous

With complex numbers

Use complex charateristic roots method. found in section 4.3

With constant coefficients

Use real characteristic roots methos. found in section 4.2

First order

Can it be intergrsted directly.

No

Use the intergrating factor technique. see hyperlink for tuturial.

Intergrating factor

Now that you have your intergrating factor, multiply both sides by it, integrate and solve for Y.

Yes

Intergrate the left side and the right side to get into the form Y= F(x)

IVP/piecewise function/step function

For these types of problems use Laplace.