Sage-Tips

Can order of differential equation be negative?

All of the derivatives in the equation are free from fractional powers, positive as well as negative if any. There shouldn’t be involvement of highest order derivative as a transcendental function, trigonometric or exponential, etc. …

When order of differential equation is not defined?

The degree of any differential equation can be found when it is in the form a polynomial; otherwise, the degree cannot be defined. Suppose in a differential equation dy/dx = tan (x + y), the degree is 1, whereas for a differential equation tan (dy/dx) = x + y, the degree is not defined.

What determines the order of a differential equation?

The order of a differential equation is determined by the highest-order derivative; the degree is determined by the highest power on a variable. The higher the order of the differential equation, the more arbitrary constants need to be added to the general solution.

Can the order of a differential equation be zero?

If the degree of a differential equation is 0, it means that the highest order derivative term of the unknown function y, has degree 0, which in turn means that there is no highest order derivative term in the given differential equation.

What is an nth order differential equation with negative n?

An nth order differential equation is by definition an equation involving at most nth order derivatives. When n is negative, it could make sense to say that an “nth order derivative” is a ” (-n)th order integral”.

How do you find the Order of the differential equation?

The order of the differential equation is the order of the highest order derivative present in the equation. Here some examples for different orders of the differential equation are given. (d 2 y/dx 2 )+ 2 (dy/dx)+y = 0. The order is 2 (dy/dt)+y = kt.

What does the negative degree of a differential equation signify?

In fractional calculus, order can be any real number. In Integer Calculus if [math]n<0[/math] we call integration. So we can say that negative degree of differential equation signifies integration.

What is the degree of a negative order of derivative?

The degree of a differential equation is usually (*) the degree of the highest ordered derivative occurring in the equation. Hence in mathematics we have not define a negative order of derivative i don’t think it makes sense the notion of ‘negative degree’.