d_leet said:It might help a bit if you told us what the differential equation was.
Saladsamurai said:Okay. Since it was given that the 3rd order diff eq is homogeneous, it is okay to assume that there is no particular solution to this, right?
And I can also assume that (m-5) is a factor of the characteristic equation. I am also assuming that it is a thrice repeated root, so [itex]y=c_1e^{5x}+c_2xe^{5x}+c_3x^2e^{5x} [/itex]
I am not so confident in this, since it is all based on assumption. Any thoughts on the validity of this?
Yes, there are several methods for solving differential equations, such as separation of variables, integrating factors, and substitution. However, the specific method used depends on the type of differential equation and its complexity.
No, not all differential equations have analytical solutions. Some may require numerical methods for approximation, while others may not have a solution at all.
An ordinary differential equation involves a single independent variable, while a partial differential equation involves multiple independent variables. The solution of a partial differential equation is a function of all the independent variables, while the solution of an ordinary differential equation is a function of a single independent variable.
Initial and boundary conditions are necessary for solving a differential equation as they provide specific values for the unknown function and its derivatives. Without these conditions, there may be an infinite number of solutions or no solution at all.
Yes, there are various software and tools available for solving differential equations, such as Matlab, Mathematica, and Wolfram Alpha. These tools use numerical methods to approximate the solution to a given differential equation.