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Solve the initial value problem x' = 3x, x(0) = -1 y' = -2x + 2y, y(0) = 5.

Solve the initial value problem x' = 3x, x(0) = -1 y' = -2x + 2y, y(0) = 5.

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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Solve the initial value problem.

**Solve the initial value problem** Given the system of differential equations: 1. \( x' = 3x \) with the initial condition \( x(0) = -1 \) 2. \( y' = -2x + 2y \) with the initial condition \( y(0) = 5 \) The solutions to the initial value problem are: - \( x(t) = -e^{3t} \) - \( y(t) = x + 1/2 + (\Theta / 2)e^{2t} \) (Note: There might be a typographical error in the expression for \( y(t) \) regarding the use of \( \Theta \) and \( x \) without proper context or values being given for them.)
Transcribed Image Text:**Solve the initial value problem** Given the system of differential equations: 1. \( x' = 3x \) with the initial condition \( x(0) = -1 \) 2. \( y' = -2x + 2y \) with the initial condition \( y(0) = 5 \) The solutions to the initial value problem are: - \( x(t) = -e^{3t} \) - \( y(t) = x + 1/2 + (\Theta / 2)e^{2t} \) (Note: There might be a typographical error in the expression for \( y(t) \) regarding the use of \( \Theta \) and \( x \) without proper context or values being given for them.)
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