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Differential Equations, Lecture 3.3: The method of undetermined coefficients
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Differential Equations, Lecture 3.3: The method of undetermined coefficients.
The general solution of a linear 2nd order ODEs has the form y(t)=y_h(t)+y_p(t), where y_h(t) solves the homogeneous equation, and y_p(t) is any particular solution. In this lecture we learn how to identify a simple a particular solution in many cases. For an ODE of the form ay''+by'+cy=f(t), we guess that y_p(t) "has the same form" as the forcing term, and then we plug this into the ODE and solve for the unknown coefficients.
The general solution of a linear 2nd order ODEs has the form y(t)=y_h(t)+y_p(t), where y_h(t) solves the homogeneous equation, and y_p(t) is any particular solution. In this lecture we learn how to identify a simple a particular solution in many cases. For an ODE of the form ay''+by'+cy=f(t), we guess that y_p(t) "has the same form" as the forcing term, and then we plug this into the ODE and solve for the unknown coefficients.
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