I have consult some good books of differential equation as well as Google but I have not found any satisfactory definition of degree of a differential equation. please give correct definition of degree of a differential equation. Also, if possible give name of books.
The degree of an ordinary differential equation (ODE) is not AFAIK a commonly used concept but the order is. The order of an ODE is just the order of the highest derivative that appears in the equation.
Some authors (see e.g. the links below) indeed define the degree of an ODE as the power of the highest-order derivative which occurs at the equation, but not all ODEs have a well-defined degree (e.g. if the highest-order derivative enters the equation in a nonpolynomial fashion, this equation obviously has no well-defined degree).
http://www.solitaryroad.com/c650.html
http://physics.oregonstate.edu/~warrenw/COURSES/ph461/H6.pdf
The degree of an ordinary differential equation (ODE) is not AFAIK a commonly used concept but the order is. The order of an ODE is just the order of the highest derivative that appears in the equation.
Some authors (see e.g. the links below) indeed define the degree of an ODE as the power of the highest-order derivative which occurs at the equation, but not all ODEs have a well-defined degree (e.g. if the highest-order derivative enters the equation in a nonpolynomial fashion, this equation obviously has no well-defined degree).
http://www.solitaryroad.com/c650.html
http://physics.oregonstate.edu/~warrenw/COURSES/ph461/H6.pdf
The order of a differential equation is the order of the highest derivative appearing in the equation.
The degree of a differential equation is given by the exponent that is raised the highest derivative that occurs in the equation
x''-2x'+3x=0 is a second order and first degree, and (x'')^3+(x')^5+2x=0 is second order and three degree
The degree of the highest order of the derivative is the degree of ODE.
Respected Sir Please Answer what is the degree and order of
e^(dy/dx) =d^2y/dx^2
The degree of an ODE is the degree of the highest derivatives, which occurs in it when the differential coefficient have been made free from radicals and fractions, if any
It is just the order of the highest derivative that appears in the equation.
Very thanks to all respected professors for answering. I wish to know that, what is the degree of (dy/dx)^2-y=0.
I also request to answer my question, not to laughing on the simplicity of the question. I wish to know some thing about the way of thinking.
The order of an ODE is just the order of the highest derivative that appears in the equation.
The degree of a differential equation is a positive integer which is power of highest order derivative term in the differential equation. In your case it is 2..
It is 2. because to find the degree of Differential equation the dependent variable must have integral power in all terms.
@ Dr. Ghosh
According to my knowledge, a differential equation of the form dy/dx=f(x,y) is of first order and first degree. The given differential differential dy/dx=square root (y) is also of the same form, that is of first order and first degree, not of degree two. Also, I request you to sent me any link for online search or any book (pdf) in which the definition of degree of an ODE is given such that the depend variable also will be free from radicals and fractions.
It may be noted that degree of a DE may or may not exist. To obtain degree of a DE first we express the differential equation as a polynomial function of the derivatives involved in it (here we don't care the exponent of unknown function e.g it may be a fraction as well). Thus the degree of a DE is the exponent of highest order derivative appearing in it provided the differential equation is made a polynomial function of the derivatives involved in it. Obviously the degree of dy/dx= square root (y) is one. The degree of sin (dy/dx)=y is not defined though the degree dy/dx=arc sin(y) is one. Also degree of dy/dx= square root (x) is one but the degree of (dy/dx)^2=x is two.
The degree of an ordinary differential equation is the highest power of highest order derivative involve in the differential equation, provided the dependent variable and its derivatives should be free from radicals (if any).
The degree of dy/dx=square root (y) is one as any diff equation of the form dy/dx=f(x, y) is of first order first degree. But according to your definition that after removing radical in dependent variable y, its degree is two that is contradiction.
@ 'S. K. Chaubey Sir
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