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Mashutka [201]
2 years ago
12

Section 5.2 Problem 6:Find the general solution

0%3D%200" id="TexFormula1" title="y'' + 6y' + 10y = 0" alt="y'' + 6y' + 10y = 0" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
mihalych1998 [28]2 years ago
4 0

Answer:

y=e^{-3t}(A\: cos\: t+B\:sin\:t)

Step-by-step explanation:

<u>Given Second-Order Homogenous Differential Equation</u>

y''+6y'+10y=0

<u>Use Auxiliary Equation</u>

<u />m^2+6m+10=0\\\\(m+3)^2+1=0\\\\(m+3)^2=-1\\\\m+3=\pm i\\\\m=-3\pm i

<u>General Solution</u>

<u />y=e^{pt}(A\: cos\: qt+B\:sin\:qt)\\\\y=e^{-3t}(A\: cos\: t+B\:sin\:t)

Note that the DE has two distinct complex solutions p\pm qi where A and B are arbitrary constants.

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