Solve the given initial value problem.
The solution of the given initial value is when and .
If the auxiliary equation has complex conjugate roots , then the general solution is given as:
Given differential equation is
Then the auxiliary equation is
Therefore, the general solution is:
Given initial conditions are and
Therefore, the solution is
Discontinuous Forcing Term. In certain physical models, the nonhomogeneous term, or forcing term, g(t) in the equation
may not be continuous but may have a jump discontinuity. If this occurs, we can still obtain a reasonable solution using the following procedure. Consider the initial value problem;
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