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">
1 answer:
Answer:
![y=e^{-3t}(A\: cos\: t+B\:sin\:t)](https://tex.z-dn.net/?f=y%3De%5E%7B-3t%7D%28A%5C%3A%20cos%5C%3A%20t%2BB%5C%3Asin%5C%3At%29)
Step-by-step explanation:
<u>Given Second-Order Homogenous Differential Equation</u>
![y''+6y'+10y=0](https://tex.z-dn.net/?f=y%27%27%2B6y%27%2B10y%3D0)
<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](https://tex.z-dn.net/?f=m%5E2%2B6m%2B10%3D0%5C%5C%5C%5C%28m%2B3%29%5E2%2B1%3D0%5C%5C%5C%5C%28m%2B3%29%5E2%3D-1%5C%5C%5C%5Cm%2B3%3D%5Cpm%20i%5C%5C%5C%5Cm%3D-3%5Cpm%20i)
<u>General Solution</u>
<u />![y=e^{pt}(A\: cos\: qt+B\:sin\:qt)\\\\y=e^{-3t}(A\: cos\: t+B\:sin\:t)](https://tex.z-dn.net/?f=y%3De%5E%7Bpt%7D%28A%5C%3A%20cos%5C%3A%20qt%2BB%5C%3Asin%5C%3Aqt%29%5C%5C%5C%5Cy%3De%5E%7B-3t%7D%28A%5C%3A%20cos%5C%3A%20t%2BB%5C%3Asin%5C%3At%29)
Note that the DE has two distinct complex solutions
where
and
are arbitrary constants.
You might be interested in
I do not know how to do this but i can tell you ^ means exponent not division. So 3^2 would be the same as ![3^{2}](https://tex.z-dn.net/?f=3%5E%7B2%7D)
|n|=3
n=+3;n=-3
|n|=14
n=+4; n=-4
|n|=1
n=+1; n=-1
Answer:
La réponse devrait être 306
Step-by-step explanation:
184.35 + 12.90 + 125 + 127.75 = P450
Answer:
-141,0.9845,62.1348
Step-by-step explanation: