Differential Equations

Is the Differential Equation 1st Order?

r

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

Yes

Can it be integrated directly

Yes

Integrate

No

Is it seperable

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

Yes

Solve by seperation of variables

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

No

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

yes

Solve by the integrating factor method

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I.Put into the form:y'+P(x)y=Q(x)II.The integrating factor will be e^(integral(P(x)dx, no +C neccessaryII.Multiply both sides by the integrating factor and integrate both sidesThe left side will become (Integrating factor)*(y)III.Solve for y

no

Approximate using Euler's method

No

Write it as a system of first order differential equations

Solve using Eigenvectors

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Please click on the globe to the right

a

Solve using Laplace Transforms

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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

Solve using undetermined coefficients

Solve using variation of parameters