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Is the Differential Equation Linear?

Yes

Is it a System of Linear Differential Equations?

It is an IVP?

Is the Differential Equation First Order?

Is the Differential Equation Second Order?

Is the Differential Equation Higher Order?

Go Back the the Beginning.

Use Laplace Transform

Is there a Driving Force?

Solve using Method of Undetermined Coefficients.

Complex Driving Force

Solve using Variation of Parameters.

Simple Driving Force?

Solve using the Method of Undetermined Coefficients.

Can you integrate it directly?

Is it Separable?

Use the Integrating Factor method to solve.

Solve by Separation of Variables

Solve by direct integration.

Solve Using Laplace Transformation Method.

Solve Using Variation of Parameters

No

OUCHIE