Second Order Differential Equation Example

Solve the following second order differential equation:

Solution

Let’s write the auxiliary equation:

Now it can be rewritten in the next form:

So, the roots are:

The general solution for the differential equation is:

Finally, we should find the unknown coefficients

2. Solve the following second order differential equation:

Solution

The auxiliary equation will be:

The roots of the auxiliary equation will be:

Thus, the solution for the differential equation is:

Using initial values:

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