Second Order Differential Equation Example

Solve the following second order differential equation:

second order differential equation

Solution

Let’s write the auxiliary equation:

second order differential equation example

Now it can be rewritten in the next form:

second order differential equation sample

So, the roots are:

second order differential equation assignment
The general solution for the differential equation is:

second order differential equation task
Finally, we should find the unknown coefficients

solution of second order differential equation

2. Solve the following second order differential equation:

analyzed solution of second order differential equation

Solution

The auxiliary equation will be:

The roots of the auxiliary equation will be:

second order differential equation examples

Thus, the solution for the differential equation is:

second order differential equation example analysis
Using initial values:

second order differential equation task analyzed

second order differential equation

second order differential equation project completed

Mathematics often becomes a major pain, especially when you have no time to do your homework. And second order differential equations will fill your nightmares, along with the imposing deadlines. That’s not how it’s supposed to be! You have to deal with this mathematical horror once and for all.

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