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Showing content from https://dlmf.nist.gov/4.7 below:

§4.7 Derivatives and Differential Equations ‣ Logarithm, Exponential, Powers ‣ Chapter 4 Elementary Functions

§4.7 Derivatives and Differential Equations Contents
  1. §4.7(i) Logarithms
  2. §4.7(ii) Exponentials and Powers
§4.7(i) Logarithms

For a nonvanishing analytic function f ⁡ ( z ) , the general solution of the differential equation

is

§4.7(ii) Exponentials and Powers

When az is a general power, ln ⁡ a is replaced by the branch of Ln ⁡ a used in constructing az .

The general solution of the differential equation

is

The general solution of the differential equation

is

where A and B are arbitrary constants.

For other differential equations see Kamke (1977, pp. 396–413).

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