Linear equation has variables raised only to first power. Differential equation has derivatives {linear differential equation, calculus}. Second-order differential equation has second derivatives. Homogeneous equation has function equal to zero.
homogeneous
Second-order first-degree linear homogeneous differential general equation is a * (d^2)x + b * dx + c = 0, where (d^2) is second differential, d is first differential, x is independent variable, and a, b, and c are coefficients. General solution is c1 * e^(r1 * x) + c2 * e^(r2 * x), where e is base of natural logarithms, c1 and c2 are constants, r1 and r2 are roots, and x is independent variable.
non-homogeneous
Second-order, first-degree linear non-homogeneous differential general equation is a * (d^2)x + b * dx = -c, with same general solution.
Mathematical Sciences>Calculus>Differential Equation>Kinds
3-Calculus-Differential Equation-Kinds
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Date Modified: 2022.0224