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Math Advanced Math Fundamentals of Differential Equations (9th Edition)

Whether the method of undetermined coefficients can be applied to find a particular solution of the equation 8 z ′ ( x ) − 2 z ( x ) = 3 x 100 e 4 x cos 25 x . Yes _ , the method of undetermined coefficients can be applied to find a particular solution of the equation 8 z ′ ( x ) − 2 z ( x ) = 3 x 100 e 4 x cos 25 x . A particular solution to the differential equation a y ″ + b y ′ + c y = C t m e α t cos β t can be obtained by the method of undetermined coefficients, where m is a nonnegative integer and β ≠ 0 . The given differential equation is 8 z ′ ( x ) − 2 z ( x ) = 3 x 100 e 4 x cos 25 x . Comparing 8 z ′ ( x ) − 2 z ( x ) = 3 x 100 e 4 x cos 25 x with a y ″ + b y ′ + c y = C t m e α t cos β t , it is observed that m = 100 . Since m is a nonnegative integer, the method of undetermined coefficients will give a particular solution. Thus, the method of undetermined coefficients can be applied to the equation 8 z ′ ( x ) − 2 z ( x ) = 3 x 100 e 4 x cos 25 x .

Whether the method of undetermined coefficients can be applied to find a particular solution of the equation 8 z ′ ( x ) − 2 z ( x ) = 3 x 100 e 4 x cos 25 x . Yes _ , the method of undetermined coefficients can be applied to find a particular solution of the equation 8 z ′ ( x ) − 2 z ( x ) = 3 x 100 e 4 x cos 25 x . A particular solution to the differential equation a y ″ + b y ′ + c y = C t m e α t cos β t can be obtained by the method of undetermined coefficients, where m is a nonnegative integer and β ≠ 0 . The given differential equation is 8 z ′ ( x ) − 2 z ( x ) = 3 x 100 e 4 x cos 25 x . Comparing 8 z ′ ( x ) − 2 z ( x ) = 3 x 100 e 4 x cos 25 x with a y ″ + b y ′ + c y = C t m e α t cos β t , it is observed that m = 100 . Since m is a nonnegative integer, the method of undetermined coefficients will give a particular solution. Thus, the method of undetermined coefficients can be applied to the equation 8 z ′ ( x ) − 2 z ( x ) = 3 x 100 e 4 x cos 25 x .

Solution Summary: The author analyzes whether the method of undetermined coefficients can be applied to find a particular solution of the equation 8zprime (x)-2z

Fundamentals of Differential Equations (9th Edition)

Fundamentals of Differential Equations (9th Edition)

9th Edition

ISBN: 9780321977069

Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Publisher: PEARSON

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Fundamentals of Differential Equations (9th Edition)

Ch. 4.1 - Verify that for b = 0 and Fext(t) = 0, equation...Ch. 4.1 - If Fext(t) = 0, equation (3) becomes my + by + ky...Ch. 4.1 - Show that if Fext(t) = 0, m = 1, k = 9, and b = 6,...Ch. 4.1 - Verify that y = sin 3t + 2 cos 3t is a solution to...Ch. 4.1 - Prob. 5E Ch. 4.1 - An external force F(t) = 2 cos 2t is applied to a...Ch. 4.1 - Prob. 7E Ch. 4.1 - In Problems 79, find a synchronous solution of the...Ch. 4.1 - In Problems 79, find a synchronous solution of the...Ch. 4.1 - Prob. 10E

Ch. 4.2 - In Problems 112, find a general solution to the...Ch. 4.2 - In Problems 112, find a general solution to the...Ch. 4.2 - Prob. 3E Ch. 4.2 - In Problems 112, find a general solution to the...Ch. 4.2 - Prob. 5E Ch. 4.2 - Prob. 6E Ch. 4.2 - Prob. 7E Ch. 4.2 - Prob. 8E Ch. 4.2 - Prob. 9E Ch. 4.2 - Prob. 10E Ch. 4.2 - In Problems 112, find a general solution to the...Ch. 4.2 - In Problems 112, find a general solution to the...Ch. 4.2 - In Problems 1320, solve the given initial value...Ch. 4.2 - In Problems 1320, solve the given initial value...Ch. 4.2 - Prob. 15E Ch. 4.2 - In Problems 1320, solve the given initial value...Ch. 4.2 - Prob. 17E Ch. 4.2 - Prob. 18E Ch. 4.2 - Prob. 19E Ch. 4.2 - In Problems 1320, solve the given initial value...Ch. 4.2 - Prob. 21E Ch. 4.2 - Prob. 22E Ch. 4.2 - Prob. 23E Ch. 4.2 - Prob. 24E Ch. 4.2 - Prob. 25E Ch. 4.2 - Prob. 26E Ch. 4.2 - In Problems 2732, use Definition 1 to determine...Ch. 4.2 - In Problems 2732, use Definition 1 to determine...Ch. 4.2 - In Problems 2732, use Definition 1 to determine...Ch. 4.2 - In Problems 2732, use Definition 1 to determine...Ch. 4.2 - Prob. 31E Ch. 4.2 - Prob. 32E Ch. 4.2 - Prob. 33E Ch. 4.2 - Prob. 34E Ch. 4.2 - Prob. 35E Ch. 4.2 - Using the definition in Problem 35, prove that if...Ch. 4.2 - Prob. 37E Ch. 4.2 - Prob. 38E Ch. 4.2 - Prob. 39E Ch. 4.2 - Prob. 40E Ch. 4.2 - In Problems 3741, find three linearly independent...Ch. 4.2 - Prob. 42E Ch. 4.2 - Prob. 43E Ch. 4.2 - Solve the initial value problem: y 2y y + 2y =...Ch. 4.2 - Prob. 45E Ch. 4.2 - Prob. 46E Ch. 4.3 - In Problems 18, the auxiliary equation for the...Ch. 4.3 - In Problems 18, the auxiliary equation for the...Ch. 4.3 - In Problems 18, the auxiliary equation for the...Ch. 4.3 - In Problems 18, the auxiliary equation for the...Ch. 4.3 - Prob. 5E Ch. 4.3 - Prob. 6E Ch. 4.3 - In Problems 18, the auxiliary equation for the...Ch. 4.3 - In Problems 18, the auxiliary equation for the...Ch. 4.3 - In Problems 920, find a general solution. 9. y 8y...Ch. 4.3 - In Problems 920, find a general solution. 10. y +...Ch. 4.3 - Prob. 11E Ch. 4.3 - Prob. 12E Ch. 4.3 - In Problems 920, find a general solution. 13. y ...Ch. 4.3 - Prob. 14E Ch. 4.3 - Prob. 15E Ch. 4.3 - Prob. 16E Ch. 4.3 - In Problems 920, find a general solution. 17. y y...Ch. 4.3 - In Problems 920, find a general solution. 18. 2y +...Ch. 4.3 - Prob. 19E Ch. 4.3 - In Problems 920, find a general solution. 20. y y...Ch. 4.3 - In Problems 2127, solve the given initial value...Ch. 4.3 - Prob. 22E Ch. 4.3 - Prob. 23E Ch. 4.3 - In Problems 2127, solve the given initial value...Ch. 4.3 - Prob. 25E Ch. 4.3 - In Problems 2127, solve the given initial value...Ch. 4.3 - Prob. 27E Ch. 4.3 - Prob. 28E Ch. 4.3 - Prob. 29E Ch. 4.3 - Prob. 30E Ch. 4.3 - Prob. 31E Ch. 4.3 - Prob. 32E Ch. 4.3 - Prob. 33E Ch. 4.3 - Prob. 34E Ch. 4.3 - Swinging Door. 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