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Use “Undetermined coefficients” method
- Solve for the roots of the characteristic equation.
- use quadratic formula
- use the the roots of the characteristic equation to find the solution of the complimentary equation
- refer back to solutions of “constant coefficient second order linear equations”
- Find a suitable general form for a “particular solution”, , that matches the “right side of the given equation” ( is the same as , which is function representing the amount of charge of a sytem).
- if the right side of the equation is , , or , then the particular solution is of the form
- since no terms in is a solution of the complimentary equation, no extra steps are necessary in deciding the form of the particular solution
- Differentiate the chosen particular solution twice to find and .
- Substitute the values of , , and into , , and .
- Simplify the new equation.
- Rearrange the terms of the equation (factoring may be necessary) so that the “left side of the equation” matches the form of the “right side of the equation”.
- Create and solve a system of equations to solve for the undetermined coefficients.
- Plug in the values of the undetermined coefficients into the chosen particular solution to determine .
- Since the steady steady state current, , is equal to , we must differentiate to solve for the steady state current of the system.