The first differential equation
is called d’Alembert’s differential equation; here and some known differentiable real functions.
If we denote , the equation is
We take as a new variable and derive the equation with respect to , getting
If the equation has the roots , , …, , then we have for all ’s, and therefore there are the special solutions
for the original equation. If , then the derived equation may be written as
which linear differential equation has the solution with the integration constant . Thus we get the general solution of d’Alembert’s equation as a parametric
of the integral curves.
|Date of creation||2013-03-22 14:31:05|
|Last modified on||2013-03-22 14:31:05|
|Last modified by||pahio (2872)|