Degree of Freedom: Maths Definition & Differential Equations

[anum]

what is meant by the degree of freedom in Mathematics? Especially in the differential equations.

 

[HOI]

It depend a lot on the specific problem. Generally, "the degrees of freedom" are the number of values that can be arbitrarily, and independently, chosen in a problem. For example, if you have a bead moving on a circular frame, each point has an (x, y) coordinate but since the point must lie on a circle, x and y are not independent- given either x or y we can calculate the other so this problem has one degree of freedom. A point that can lie anywhere on a given plane has three two degrees of freedom because a plane is two dimensional. A point that can be anywhere in three dimensional space has three degrees of freedom. On the other hand, a "projectile" problem, where an object is launched along some trajectory in three dimensional space is one dimensional since the (x, y, z) position of the projectile is determined by the single variable, t, the time.