By Henry M. Paynter

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The problem is reduced to Eq. 7). y/ > 0. Therefore, a set of all vectors defines a vector field. y/ D 0 are called singular points of the vector field (or its equilibrium positions in the case when we deal with time). Having drawn the vector field of the given Eq. 12) one may draw schematically the integral curves. 5. 6. 2 Separable Equation 19 In what follows we proceed with a few examples of real-world applications. 7. A particle of mass m is subjected to action of a constant force, and it moves with the constant acceleration a.

5. 6. 2 Separable Equation 19 In what follows we proceed with a few examples of real-world applications. 7. A particle of mass m is subjected to action of a constant force, and it moves with the constant acceleration a. The viscous damping of the surrounding medium is c. 0/ D 0. 8. A meteorite of mass M starts to move from its rest position into the Earth centre linearly from the height h (Fig. 1). Determine the meteorite velocity, when it touches the Earth surface assuming the Earth radius R. Fig.

Find dy dt assuming that the reaction velocity is proportional to the product of reacting masses. ˇ y/; p > 0; and p is the proportionality coefficient. e. 0/ D 0, therefore C D 1=˛. x; y/ is called homogenous of order k, if for all property holds [208] F . 14) are homogenous of order k D 0; 1; 2;, respectively. x; y/ is of order zero. 16) is called homogeneous, if the function F1 , F2 are homogeneous of the same order. In the case of a homogeneous equation the introduction of a new variable y D zx allows to get en equation with separable variables.

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