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# Solving Second Order Linear Differential Equation

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Find the transient and steady-state currents in the RLC circuit with L= 5 henrys, R= 10 ohms, C=0.1 farad and E=25sint volts.
L(d^2Q/dt^2) + R(dQ/dt) + 1/C*Q = E refer to attachment for better formula representation.

https://brainmass.com/math/ordinary-differential-equations/solving-second-order-linear-differential-equation-576679

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Solution:
The differential equation will be

The characteristic equation is

so the complementary solution will be

This is called transient part of the solution.
Let particular solutions be

This gives
A+2B = 0
-2A + B = 5
After solving, we will get
B = 1, A = -2
Thus,
This is called steady state term of the solution.
The general solution is

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