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Suoppose that f is a differentiable function satisfying the following differential equation: (*) f" – 2 · f" – f' +2 · fƒ = 0. 1. Find a 3 x 3 matrix A € Mat33(R) such that (f, f', f")* =: f is a solution to the system f' = A ·f. 2. Diagonalize A and find the general solution to the following system of differential equations: r' = A · x. Hint: If you find that your A is not diagonalizable, then you have made a mistake somewhere. 3. Use parts 1 and 2 to find the general solution for f. 4. Suppose furthermore that f(0) = f'(0) = 1 = f"(0) - 1. Find f.

Suoppose that f is a differentiable function satisfying the following differential equation: (*) f" – 2 · f" – f' +2 · fƒ = 0. 1. Find a 3 x 3 matrix A € Mat33(R) such that (f, f', f")* =: f is a solution to the system f' = A ·f. 2. Diagonalize A and find the general solution to the following system of differential equations: r' = A · x. Hint: If you find that your A is not diagonalizable, then you have made a mistake somewhere. 3. Use parts 1 and 2 to find the general solution for f. 4. Suppose furthermore that f(0) = f'(0) = 1 = f"(0) - 1. Find f.

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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Suoppose that f is a differentiable function satisfying the following differential equation: (+) f" – 2 · f" –- f' + 2 · f = 0. 1. Find a 3 x 3 matrix A € Mat3,3 (R) such that (f, f', f")' =: f is a solution to the system f' = A· f. 2. Diagonalize A and find the general solution to the following system of differential equations: r' = A· x. Hint: If you find that your A is not diagonalizable, then you have made a mistake somewhere. 3. Use parts 1 and 2 to find the general solution for f. 4. Suppose furthermore that f(0) = f'(0) = 1= f"(0) – 1. Find f.
Transcribed Image Text:Suoppose that f is a differentiable function satisfying the following differential equation: (+) f" – 2 · f" –- f' + 2 · f = 0. 1. Find a 3 x 3 matrix A € Mat3,3 (R) such that (f, f', f")' =: f is a solution to the system f' = A· f. 2. Diagonalize A and find the general solution to the following system of differential equations: r' = A· x. Hint: If you find that your A is not diagonalizable, then you have made a mistake somewhere. 3. Use parts 1 and 2 to find the general solution for f. 4. Suppose furthermore that f(0) = f'(0) = 1= f"(0) – 1. Find f.
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