Linear differential equation problems

    • [DOC File]MM405A : Differential Equations

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      Linear systems, Matrix method for homogeneous first order system of linear differential equations, fundamental set and fundamental matrix, Wronskian of a system, Method of variation of constants for a nonhomogeneous system with constant coefficients, nth order differential equation equivalent to a first order system (Relevant topics from the ...

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    • [DOC File]Finite Difference Method for Solving Differential Equations

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      By writing the resulting linear equation at different points at which the ordinary differential equation is valid, we get simultaneous linear equations that can be solved by using techniques such as Gaussian elimination, the Gauss-Siedel method, etc. Substituting these approximations from Equations (E2.9) and (E2.10) in Equation (E2.3) (E2.11 ...

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    • [DOC File]SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS

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      2 Read the problems 20 on page 71 of the textbook for some important general properties of homogeneous and nonhomogeneous linear differential equations. Linear Independence (p. 68 of the Textbook) Two functions, y1(x) and y2(x), are linearly independent on an interval [x0, x1] whenever the relation c1 y1(x) + c2 y2(x) = 0 for all x in the ...

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    • [DOC File]FIRST-ORDER DIFFERENTIAL EQUATIONS

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      Considering it as a linear equation, we must first compute the integrating factor e= e= et/50. Multiplying the differential equation by this factor gives. et/50 = 6 et/50. From this, by integration, we obtain. Q et/50 = 300 et/50 + c. or Q = 300 + c e–t/50. Substituting the initial conditions t = 0, Q = 50, we find c = 250

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    • [DOC File]A Primer for Ordinary Differential Equations

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      An equation that consists of derivatives is called a differential equation. Differential equations have applications in all areas of science and engineering. Mathematical formulation of most of the physical and engineering problems leads to differential equations.

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    • [DOC File]Differential Equations Final Practice Exam

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      (Final Fall 1998 Problem 6) For the linear system of differential equations , . Solutions. a) b) eigenvalues . c) are the eigenvectors (utilizing the fact the eigenvectors will be complex conjugates because the eigenvalues are complex numbers) Note that any multiple (where r can be any complex number) would be an acceptable solution.

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    • [DOC File]CHAPTER 1 FIRST-ORDER DIFFERENTIAL EQUATIONS

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      Then, every solution of this differential equation on I is a linear combination of and . 7. Definition: Let and be solutions of on an open interval I. (1) and form a fundamental set (or a basis) of solutions on I if and are linearly independent on I. (2) When and form a fundamental set of solutions, we call , with and arbitrary constants, the ...

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    • [DOC File]Mat 275 Modern Differential Equations

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      A second order differential equation in the (unknown) function is one of the form . This differential equation is said to be linear provided that G is linear in the dependent variable y and its derivatives . The DE is a second order linear DE. On the other hand is not a second order linear FE because of the non linear term .

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    • [DOC File]Fundamentals of Engineering Exam Sample Questions

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      Which of the following choices is the general solution to this differential equation: ? b. c. d. If D is the differential operator, then the general solution to . A particle traveled in a straight line in such a way that its distance S from a given point on that line after time t was . …

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    • [DOC File]Partial Differential Equations in Two or More Dimensions

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      The FFT method is applicable to linear boundary-value problems in domains where at least one of the spatial dimensions is finite. Let ( = ((r, t) be the field variable (e.g., temperature or concentration), and let L be a differential operator which contains one or more spatial derivatives and perhaps also a …

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