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Find the general real solution of this system of differential equations x' y' = x 2y 2x + y =

Find the general real solution of this system of differential equations x' y' = x 2y 2x + 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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Find the general real solution of this system of differential equations x' y' x(t) = c_1 e^(t+it) - c_2 e^(t+it) y(t) = c_1 e^(t+it) + c_2 e^(t+it) x(t) = c_1 e^(t+it) + c_2 e^(t+it) y(t) = c_1 e^(t+it) + c_2 e^(t+it) x(t) = c_1 e^t cos(t) - c_2 e^t sin(t) = = y(t) = c_1 e^t sin(t) + c_2 e^t cos(t) x(t) = c_1 e^t cos(t) + c_2 e^t sin(t) y(t) = c_1 e^t sin(t) + c_2 e^t cos(t) x - 2y 2x + y
Transcribed Image Text:Find the general real solution of this system of differential equations x' y' x(t) = c_1 e^(t+it) - c_2 e^(t+it) y(t) = c_1 e^(t+it) + c_2 e^(t+it) x(t) = c_1 e^(t+it) + c_2 e^(t+it) y(t) = c_1 e^(t+it) + c_2 e^(t+it) x(t) = c_1 e^t cos(t) - c_2 e^t sin(t) = = y(t) = c_1 e^t sin(t) + c_2 e^t cos(t) x(t) = c_1 e^t cos(t) + c_2 e^t sin(t) y(t) = c_1 e^t sin(t) + c_2 e^t cos(t) x - 2y 2x + y
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