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https://texercises.com/exercise/third-order-differential-equation/
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Exercise:
Convert the following linear third order differential o a system of first-order differential s and derive the corresponding matrix: y''' -y''+y'+y

Solution:
We roduce new functions z and w as follows: z y' w z'y'' The system can then be written as y' z z' w w' w-z-y The corresponding matrix is bf A leftmatrix & & & & - & - & matrixright i.e. the system can be written as fracddxleftmatrixy z wmatrixright bf Aleftmatrixy z wmatrixright
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Exercise:
Convert the following linear third order differential o a system of first-order differential s and derive the corresponding matrix: y''' -y''+y'+y

Solution:
We roduce new functions z and w as follows: z y' w z'y'' The system can then be written as y' z z' w w' w-z-y The corresponding matrix is bf A leftmatrix & & & & - & - & matrixright i.e. the system can be written as fracddxleftmatrixy z wmatrixright bf Aleftmatrixy z wmatrixright
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Differential equations
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linear differential equation
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ENG (English)
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Calculative / Quantity
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