释义 |
Euler Differential EquationThe 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
Then is given by
which is a constant. Therefore, the equation becomes a second-order ODE with constant Coefficients
 | (10) |
Define
and
The solutions are
In terms of the original variable ,
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