Consider the system of differential equations dx dt -5y x(t): y(t) = dy dt = −52. Convert this system to a second order differential equation in y by differentiating the second equation with respect to t and substituting for a from the first equation. Solve the equation you obtained for y as a function of t; hence find x as a function of t. If we also require x(0) = 2 and y(0) = 1, what are x and y?
Consider the system of differential equations dx dt -5y x(t): y(t) = dy dt = −52. Convert this system to a second order differential equation in y by differentiating the second equation with respect to t and substituting for a from the first equation. Solve the equation you obtained for y as a function of t; hence find x as a function of t. If we also require x(0) = 2 and y(0) = 1, what are x and y?
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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Question
![Consider the system of differential equations
dx
dt
- 5y
←
dy
dt
-5x.
Convert this system to a second order differential equation in y by differentiating the second equation with respect to t and
substituting for x from the first equation.
X
Solve the equation you obtained for y as a function of t; hence find x as a function of t. If we also require x(0) = 2 and
y(0) = 1, what are x and y?
x (t) =
y(t) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb154af4-0384-48be-b4dd-887afc51ba51%2F75e69cbd-9b06-4d32-a51c-d84c6f406716%2Ffbpfak_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the system of differential equations
dx
dt
- 5y
←
dy
dt
-5x.
Convert this system to a second order differential equation in y by differentiating the second equation with respect to t and
substituting for x from the first equation.
X
Solve the equation you obtained for y as a function of t; hence find x as a function of t. If we also require x(0) = 2 and
y(0) = 1, what are x and y?
x (t) =
y(t) =
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