A degree of a differential equation is the highest power of highest order of a differential term of the equation.
For example,
5(d^4 x/dx^4) - (dx/dx)^2 =7
Here 5(d^4x/dx^2) has the highest order and so the degree will be it's power which is 1.
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The degree of a differential equation is the POWER of the derivative of the highest order. Using f' to denote df/fx, f'' to denote d2f/dx2 (I hate this browser!!!), and so on, an equation of the form (f'')^2 + (f')^3 - x^4 = 17 is of second degree.
ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.
It is the solution of a differential equation without there being any restrictions on the variables (No boundary conditions are given). Presence of arbitrary constants indicates a general solution, the number of arbitrary constants depending on the order of the differential equation.
Yes, it is.
An Airy equation is an equation in mathematics, the simplest second-order linear differential equation with a turning point.