“Euler Differential Equation”的概念、定义、习题解题方法及翻译-数学辞典

单词

Euler Differential Equation

释义

Euler Differential Equation

The general nonhomogeneous equation is

(1)

The homogeneous equation is

(2)

(3)

Now attempt to convert the equation from

(4)

to one with constant Coefficients

(5)

by using the standard transformation for linear Second-Order Ordinary Differential Equations. Comparing (3) and (5), the functions

and

are

(6)

(7)

Let

and define


			(8)

Then

is given by

which is a constant. Therefore, the equation becomes a second-order ODE with constant Coefficients

(10)

Define

and

			(13)
			(14)

The solutions are


			(15)

In terms of the original variable

(16)

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