Differensiallikningen

Differensiallikningen is a mathematical equation that relates a function with one or more of its derivatives. These equations are fundamental to describing and modeling phenomena in science, engineering, economics, and many other fields where change is involved. The unknown in a differential equation is typically a function, not a number.

The order of a differential equation is determined by the highest order derivative that appears in the equation. For example, an equation involving only the first derivative is a first-order differential equation, while one involving the second derivative is a second-order differential equation.

Differential equations can be classified as either ordinary differential equations (ODEs) or partial differential equations (PDEs). ODEs involve functions of a single independent variable and their derivatives. PDEs, on the other hand, involve functions of multiple independent variables and their partial derivatives.

Solving a differential equation means finding the function or functions that satisfy the equation. This can be a complex process, and there is no single method that works for all types of differential equations. Analytical methods aim to find exact solutions, often in terms of known functions. Numerical methods, when analytical solutions are not feasible, approximate the solutions using computational techniques. The study of differential equations and their solutions is a vast and important area of mathematics.