Euler Equation Solutions
Description
Euler's Differential Equation is a regular differential equation with a singular point at . The second order form of the equation is . The solutions are found by substituting into the differential equation with and .
After simplifying a characteristic equation of results. With a solution of . Then depending on the value inside the radical , the two solutions are:
For the case the Euler Identity, , Power rule, , and real and imaginary parts must both be solutions.
The illustration below shows the two fundamental solutions where the coefficients and can be adjusted with the sliders.