Differential Equations

If No

Are any initial conditions given?

If No

??????

Approximate using Euler's Method

If yes

Try Laplace Transform

If Yes

Is Diffential Equation First Order?

If Yes

Can you Integrate Directly?

If Yes

Solve by Direct Integration

If No

Is Differential Equation Separable?

If Yes

Solve Using Separation of Variables

If No

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

If Yes

Solve Using Integrating Factor Method

If No

Are Initial conditions given?

If Yes

Solve Using Laplace Transformations

If No

Try Method of Undetermined Coefficients

If No

Is Differential Equation Second Order?

If Yes

Are Intial Conditions Given?

If No

Solve Using Method of Undertermined Coefficients

Solve Using Variation of Parameters

If Yes

Solve Using Laplace Transforms

If No

Can Differential Equation be Written as a Sysetm of First Order Differential Equations?

If Yes

Solve Using Eigenvalues and Eigenvectors

If No

Are Intial Conditions Given?

If Yes

Solve Using Laplace Transforms

If No

Solve Using Method of Undetermined Coefficients