Answer to Question #122624 in Differential Equations for NILAM JYOTI DAS

Question

What is the standard form of homogeneous differential equation of order n.

Answer 1

HOMOGENEOUS DIFFERENTIAL EQUATION

An equation of the form

xⁿ$\frac {d^ny}{dx^n}$ + P₁x^n-1$\frac {d^{n-1}y}{dx^{n-1}}$ + P₂x^n-2 $\frac {d^{n-2}y}{dx^{n-2}}$ + ............+ P_n-1x$\frac {dy}{dx}$ +P_ny= X, where P₁, P₂, P₃, ......,P_n are constants and X is a function of x alone , is homogeneous differential equation of order n .

This is the standard form of homogeneous differential equation of order n .