By F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester

ISBN-10: 1852338962

ISBN-13: 9781852338961

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2. Find the particular solution that satisﬁes the initial conditions y(0) = 2, y (0) = 0. 11 e6x + Ax 2 + B sin x + C cos x is a solution of the 5. Find constants A, B, and C such that 18 − 14 x + 296 IVP y − 6y = 3 − cos x, y(0) = 0, y (0) = 0, y (0) = 1. B 1. A particle moves along the x-axis so that its velocity at any time t ≥ 0 is given by v(t) = 1/(t 2 + 1). Assuming that the particle is at the origin initially, show that it will never get past x = π/2. 21 22 CH A P T E R 1: Introduction to Differential Equations 2.

2. 2. Find the particular solution that satisﬁes the initial conditions y(0) = 1, y (0) = 0, y (0) = 1, and y (0) = 6. ] 3. 2. Find the particular solution that satisﬁes the initial condition r(0) = 0. ) 4. 2. Find the particular solution that satisﬁes the initial conditions y(0) = 2, y (0) = 0. 11 e6x + Ax 2 + B sin x + C cos x is a solution of the 5. Find constants A, B, and C such that 18 − 14 x + 296 IVP y − 6y = 3 − cos x, y(0) = 0, y (0) = 0, y (0) = 1. B 1. A particle moves along the x-axis so that its velocity at any time t ≥ 0 is given by v(t) = 1/(t 2 + 1).

The calculations and manipulations involved in the next example may seem tedious, but they should remind you of things you have seen in previous classes. The analysis at the end of the example should convince you that a graphical approach can be enlightening. 7 A Model of a Bimolecular Chemical Reaction Most chemical reactions can be viewed as interactions between two molecules that undergo a change and result in a new product. The rate of a reaction, therefore, depends on the number of interactions or collisions, which in turn depends on the concentrations (in moles per liter) of both types of molecules.

### A Modern Introduction to Differential Equations by F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester

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