Is Your Differential Equation Linear?

Non-Linear

Were initial conditions given?
Example: y(0)=1, y'(0)=0

Solve Using Laplace

Does the function contain an exponential and can be placed in a similar order to:
y' = (r1 * x) + C*e^(r2*t) ?

Solve Using Variation of Parameters

Is it a second order differential equation equal to an exponent, constant or trig function?

Solve using Undetermined Coefficients

Is it in the form of a matrix/system of equations?

Solve using Eigen Vectors/Values

Linear

Can It be put in the form:
y' + p(t)*y = f(t)?

Use the integrating factor to solve.

Can the Variables be separated to all t on one side and y on the other?
ex: (2y)dy = (1/t)dt

Solve by separation of variables!

Can the Equation be integrated Directly?

Integrate Directly!

Were initial conditions given?
Example: y(0)=1, y'(0)=0

Solve Using Laplace