Abstract
A new method for solving ordinary differential equations is suggested. As it is shown the differential equation can be solved not only by means of integration its differentiation as well. The developed method is applied for consideration of corresponding equations for the exponential and trigonometric functions. In the framework of the developed method the simple approach for derivation of Taylor series of a function is demonstrated. Based on the geometric definition the connections between trigonometric functions and their derivatives are obtained as well. The well-known Euler formula is also produced, which establishes a connection between trigonometric and exponential functions.
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