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Categorii: Tot - laplace - linear - separation - conditions

realizată de Luke Berhold 11 ani în urmă

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Differential Equations

When determining whether a differential equation is linear, one should check if it can be expressed in the form y' + p(t)*y = f(t). If it can, it is linear, and methods such as separation of variables, direct integration, or using an integrating factor can be applied.

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) + Ce^(r2t) ?

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