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Consider the system of differential equations dz dt x(t) = y(t) = dy dt -5y 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. -5x. Solve the equation you obtained for y as a function of t; hence find as a function of t. If we also require (0) = 2 and y(0) = 5, what are a and y?

Consider the system of differential equations dz dt x(t) = y(t) = dy dt -5y 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. -5x. Solve the equation you obtained for y as a function of t; hence find as a function of t. If we also require (0) = 2 and y(0) = 5, what are a and y?

Advanced Engineering Mathematics
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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Consider the system of differential equations da dt x(t) = y(t) = dy dt -5y 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. || -5x. Solve the equation you obtained for y as a function of t; hence find x as a function of t. If we also require (0) = 2 and y(0) = 5, what are a and y?
Transcribed Image Text:Consider the system of differential equations da dt x(t) = y(t) = dy dt -5y 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. || -5x. Solve the equation you obtained for y as a function of t; hence find x as a function of t. If we also require (0) = 2 and y(0) = 5, what are a and y?
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