Differential Equations

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Differential Equations

Is the Differential Equation 1st Order?

1st Order: the right side of the equation = 0

Solve using variation of parameters

Solve using undetermined coefficients

Solve using Laplace Transforms

Take the Laplace and put in terms of L{f(t)}

Refer to the back page of the book and match it to one of the premade equations in order to switch back to the f(t) domain

Write it as a system of first order differential equations

Solve using Eigenvectors

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Yes

Can it be integrated directly

No

Is it seperable

Seperable: where you can separate the variables to opposite sides of the equal sign and integrate

Can it be written in the form y'+p(t)=f(t)

no

Approximate using Euler's method

yes

Solve by the integrating factor method

I.Put into the form:

y'+P(x)y=Q(x)

II.The integrating factor will be e^(integral(P(x)dx, no +C neccessary

II.Multiply both sides by the integrating factor and integrate both sides

The left side will become (Integrating factor)*(y)

III.Solve for y

Solve by seperation of variables

I.Put all of one variable ie y,dy on one side and all of the other variables ie x, dx on the other

II.Integrate

Integrate