Differential Equations

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Differential Equations

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Is Your Differential Equation Linear?

Linear

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

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

Can the Equation be integrated Directly?

Try Checking The Non-Linear Side!

Integrate Directly!

Solve by separation of variables!

Use the integrating factor to solve.

Non-Linear

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

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

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

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

Try Checking the Linear Side!

Solve using Eigen Vectors/Values

Solve using Undetermined Coefficients

Solve Using Variation of Parameters

Solve Using Laplace