Linear Differential Equations Definition An equation containing a variable, its derivative and a few more functions of degree one is called a linear differential equation. The standard form of representing a linear differential equation is dy / dx + Py = Q. In this equation, x is an independent variable, and y is the dependent variable. We find derivatives of dependent variables only with respect to an independent variable. General solution formula of a linear differential equation The general solution of the differential equation dy / x + Py = Q is given by: y . (I.F) = ∫(Q . (I.F) . dx) + Cy . (I.F) = ∫(Q . (I.F) . dx) + C Here, I.F. is the integrating factor and is given by: e^ ∫P . dx Homogeneous differential equation A function f(x, y) in x and y is said to be a homogeneous function if the degree of each term in the function is constant (say p). In general, a homogeneous function ƒ(x, y) of degree n is expressible as: ƒ(x, y) = λ^n ƒ(y/x) Homogeneous differ...
