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HELP-solving differential equation RL- RLC

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Ratchit

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I am trying to solve the questions below could you help me ?
It looks like the OP ran away from his question. Therefore, I will do the first problem just to show those unfamiliar with differential equations (DE) a glimpse of how certain DEs are solved by the separation of variables. As the circuit is shown, the capacitor is energized to 8 volts before the switch is opened. The DE's are determined and solved below. The output voltage is one-third the capacitor voltage.

marten1.JPG
Next we plot the voltage for 3 seconds.

martin2.JPG
Ratch
 
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