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Masja [62]
3 years ago
5

2. Without solving the systems, explain why the following systems must have the same solution.

Mathematics
2 answers:
tino4ka555 [31]3 years ago
5 0
Because when you simplify system b, it becomes the same as system A
Musya8 [376]3 years ago
4 0
System multiplied by 2= system b
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Question 3 Unsaved
bazaltina [42]

Answer:

Step-by-step explanation:

DE given is

y''+8y'+15y=0, y(0)=0, y'(0)=1

Take Laplace on the DE

We get

s^2 Y(s) -sY(0) -y'(0)+8(sY(s)-y(0))+15Y(s) =0\\s^2 Y(s) -s(0) -1+8(sY(s)-0)+15Y(s) =0\\Y(s)(s^2+8s+15)-1=0\\Y(s) = \frac{1}{s^2+8s+15}

Simplify to get

Y(s) = \frac{1}{2}[ {\frac{1}{s+3} -\frac{1}{s+5} }]

Take inverse

y(t) = \frac{e^{-3t} -e^{-5t}}{2}

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