Differential Equations

A differential equation is an equation

A differential equation is an equation that contains derivatives of a function. Examples include dy/dx = cos x, d²y/dx² + k²y = 0. The equation relate

Order is the highest derivative present

Order is the highest derivative present (e.g., d²y/dx² means order 2). Degree is the power of the highest order derivative when the equation is polyno

Process of creating differential equations by

Process of creating differential equations by eliminating arbitrary constants through differentiation. For y = ax², differentiate to get dy/dx = 2ax,

Method where variables x and y

Method where variables x and y can be separated to opposite sides: f(x)dx = g(y)dy. Integrate both sides separately. Example: dy/dx = xy becomes dy/y

Equations where all terms have

Equations where all terms have the same degree when expressed as polynomials in x, y, and dy/dx. Solved using substitution y = vx or x = vy. Example: