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Chapter 6 Linear Systems of Differential Equations “Do not worry too much about your difculties in mathematics, I can assure you that mine are still greater.” - Albert Einstein (1879-1955) 6.1 Linear Systems 6.1.1 Coupled Oscillators In Section 3.5 we saw that thenumericalsolutionofsecondorderequa- m tions, or higher, can be cast into systems of rst order equations. Such sys- tems are typically coupled in the sense that the solution of at least one of k the equations in the system depends on knowing one of the other solutions in the system. In many physical systems ...
PROBLEM SET 21: SEPARABLE DIFFERENTIAL EQUATIONS Note: Most of the problems were taken from the textbook [1]. Problem 1. Solve the dierential equations. dy √ a) dx = x y; Problem 2. Find the solutions of the next dierential equations with specied initial values. a) dy = xsinx, y(0) = −1; dx y References [1] J. Stewart: Single Variable Calculus 8th Edition, Cengage Learning, Boston 2015. 1 ...
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