dz dt 3x – 2y fip dt 9x - 3y %3D z(0) = 1 %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Power Operation
Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus.
Exponents
The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.
Question
![Find the solution to the following system of differential equations. Express your final answer in real form!
\[
\begin{cases}
\frac{dx}{dt} = 3x - 2y \\
\frac{dy}{dt} = 9x - 3y \\
x(0) = 1 \\
y(0) = -3
\end{cases}
\]
This system consists of two first-order linear differential equations with given initial conditions for \(x\) and \(y\) at \(t = 0\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56661073-d5cb-4d6d-af43-dff77ec9898b%2Fddb2757a-aa17-4f1f-a200-919e5949f0ad%2Fpqeorhp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the solution to the following system of differential equations. Express your final answer in real form!
\[
\begin{cases}
\frac{dx}{dt} = 3x - 2y \\
\frac{dy}{dt} = 9x - 3y \\
x(0) = 1 \\
y(0) = -3
\end{cases}
\]
This system consists of two first-order linear differential equations with given initial conditions for \(x\) and \(y\) at \(t = 0\).
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