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HW4SOL-s09-correct

# Y rewrite the equation y therefore w y y y y 26 y t is

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Unformatted text preview: y ′′ p t y ′ p ty p ty p t y′ p t y ′′ p ty p t y ′ p t y ′′ Multiply the first raw by p t , multiply the second raw by p t and multiply the last row by p t . p ty p ty p ty ′ ′ p ty p t y′ p tp tp tW p ty p t y ′′ p t y ′′ p t y ′′ Therefore, 1p t p t W′ p t p t p t W. As long as the coefficients are not zero, we p t W. obtain W ′ (c) From (b) dW t dt Therefore, W y ,y ,y (d) t e , where is an integral constant. y y′ W′ y , y , ,y y y Repeat the process in (c), we can obtain p tp t , which give the equation dW t dt Therefore, Wy, #22. y Rewrite the equation. y Therefore, W y ,y ,y ,y #26. y t is a solution of y ′′′ p t y ′′ p t y ′′ p ty 0 t e 0y 0y ′′ pt 0y ′ 0 y 0 y 0 ,y t e , where is an integral constant. pWt p t W′ p tp tp t p tW y y y y′ y y y y′ y y′ y y pWt y y′ y t υ t y′ t υ t y t υ′ t y ′′ y ′′′ y ′′ t υ t y ′′′ t υ t 2y ′ t υ′ t 3y ′′ t υ′ t y t υ′ ′ t 3y ′ t υ′′ t y t υ′′ ′ t Substitute those into the differential equation y ′′′ t υ t 3y ′′ t υ′ t 3y ′ t υ′′ t ′ y t υ′′ t ′ p t y ′′ t υ t p t y ′ t υ t Reorder the equation. y υ′′′ py 3y ′ υ′′ 3y ′′ 2y ′ t υ′ t y t υ′ t y t υ′ t p ty 0 2p y ′ py υ ′ y ′′′ p y ′′ p y′ py υ 0 Since y is a solution of the differential equation, υ-term vanishes. Therefore, y υ′′′ py 3y ′ υ′′ 3y ′′ 2p y ′ py υ ′ 0 Chapter 4.2 #6. –1 1 √2 , sin θ –1 #9. 1 Writing t...
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