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DE Method Summary

1.

Determine the initial conditions (capacitor voltage or inductor current at time t=0^-). Using the continuity principle, determine these values at time t=0⁺.

2.

For second order problems, if necessary, determine any other required initial conditions, such as capacitor current and inductor voltage (these may be discontinuous at time 0).

3.

Using Ohm's law for capacitors or inductors and KCL/KVL, determine an equation for the current or voltage of interest. Obtain a differential equation from this.

4.

Find the homogeneous solution of the differential equation. The constants are not determined yet.

5.

Find the particular solution of the differential equation (the initial conditions are not used yet!).

6.

Form the total solution, using the initial conditions to determine the constants in the homogeneous solution.

7.

Check your answer.

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