recent
أخبار ساخنة

Degree vs Order

Home


Degree vs Order


This article aim to distinguish between the two concepts: Degree & Order. 
Many may ask are degree and order the same concept or not ? In fact, they are both related to differential equation (DE), because differential equations are often classified with respect to order and degree. 

Degree of DE: is the power of the highest order derivative in the equation. 

Order of DE: is the order of the highest order derivative existed in the equation. 
Examples 1:  

\(\frac{\partial^2 y}{\partial x^2} -5x\left ( \frac{\partial y}{\partial x} \right )^{4} e^{x} = \frac{\partial y}{\partial x}\) has order 3 and degree 1.
 
Examples 2: 

\(\left (\frac{\partial^2 y}{\partial x^2} \right ) ^{3} - \frac{\partial y}{\partial x} = cos(x)\) has order 2 and degree 3.

Examples 3: 

\({y}'' - xy = \left ({y}' \right )^{4}\) has order 2 and degree 1.

Examples 4: 

\( x\left ( \frac{\partial^2 y}{\partial x^2} \right )^{3} \frac{\partial y}{\partial x} - 7e^{x}\left ( \frac{\partial^2 y}{\partial x^2} \right )+yln(x) = 5 \) has order 3 and degree 2. 

Examples 5: 

This Example illustrate the weakness of definition in term of degree .i.e 

\(e^{\frac{\partial y}{\partial x}} + cos\left ( x\frac{\partial^2 y}{\partial x^2} \right ) + tan\left ( \frac{\partial^3 y}{\partial x^3} \right ) + 3xy = 0\) which has order 3 and no degree can be determined. 

Thus, from the last example we notice that despite the above definition of order is complete, the degree is not so.          


Be one of "Math212" Followers

Blog Archive

Search ...

Comments

Recent

Popular Posts

Image

Limit Point and Closure

Definition of Limit Point In Real analysis: Let \(S\) \(\in\) \(\mathbb{R}\) be any set, and let \(x\) \(\in\…

Featured

google-playkhamsatmostaqltradent