Let V be the set of all solutions of the differential equation y"(t) - 4y"(t) + 4y' (t) = 0 which satisfy y'(0) = 0. It is known that V is a vector space with dimension dim(V) = 2. Find a basis (y₁ (1), y2(t)} for V.
Let V be the set of all solutions of the differential equation y"(t) - 4y"(t) + 4y' (t) = 0 which satisfy y'(0) = 0. It is known that V is a vector space with dimension dim(V) = 2. Find a basis (y₁ (1), y2(t)} for V.
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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![Let \( V \) be the set of all solutions of the differential equation
\[ y'''(t) - 4y''(t) + 4y'(t) = 0 \]
which satisfy \( y'(0) = 0 \). It is known that \( V \) is a vector space with dimension \( \dim(V) = 2 \).
Find a basis \(\{y_1(t), y_2(t)\}\) for \( V \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff72dbd1a-89a3-4722-b0fb-ff5be11bbf8a%2F8f38adf3-409f-46b5-b423-f57f2d8f197d%2Fh5zrb74_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( V \) be the set of all solutions of the differential equation
\[ y'''(t) - 4y''(t) + 4y'(t) = 0 \]
which satisfy \( y'(0) = 0 \). It is known that \( V \) is a vector space with dimension \( \dim(V) = 2 \).
Find a basis \(\{y_1(t), y_2(t)\}\) for \( V \).
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