How would I solve the following equation d^2x/dt^2 + 5dx/dt + 6x = 0
Our given equation is d2x/dt2 + 5dx/dt + 6x = 0, which we need to recognise as a second order differential equation. Therefore we need to begin by solving the auxilary funtion m2+5m +6= 0. ( Side note: Most of the mathematical equations we solve are expressed in x and y, but in this equation it's expressed in terms of x and t, where x is the dependent variable). Solving the auxiliary funtion gives us values of -3&-2 for m. Because these are real values that are not equal to each other we can use the complimentary funtion y= Aect + Bedt where y is the dependent variable, t is our independent variable and A&B are constants of intergration. If we plug in our values the auxiliary funtion becaomes x = Ae-3t+Be-2t. Which is our final answer.
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