1 / 13

Order and Degree of Ordinary Differential Equations

Definition of Order and Degree. Solved problems. What will be the degree of the differential equation when fractional powers cannot be eliminated? Why is the degree of differential equation involving log, exponent and trigonometry functions not defined?<br>

AMINUL
Download Presentation

Order and Degree of Ordinary Differential Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Order and Degree of Ordinary Differential Equations Md. Aminul Islam

  2. Successive Derivatives …………………………………………………………….. Note: power of derivative can’t change its order

  3. Definition of Order The order of a differential equation is the order of the highest order derivative present in the equation. • First find the derivative • Pick the highest one • Take the order of the highest one To find the order

  4. Example-1: Findthe order of Solution: Here the highest order derivative present in the given differential equation is and its order is 2 So the order of the given differential equation is 2

  5. Solution: Here the highest order derivative present in the given differential equation is and its order is 1. So the order of the given differential equation is 1

  6. Definition of Degree The degree of a differential equation is the highest power of highest order derivative when the differential equation is a polynomial equation in derivatives which are free from fractions and radicals To find the degree • Check whether the given diff. eqn. is a polynomial in derivatives or not • Check whether derivatives are free from fractions and radicals or not • Find the highest order derivative and take its power or degree

  7. Example-3: Findthe degree of Solution: Here the highest order derivative present in the given differential equation is and its power is 1 So the degree of the given differential equation is 1

  8. Example-4: Findthe degree of Solution:Given equation is Here the highest order derivative present in the given differential equation is and its power is 2 So the degree of the given differential equation is 2

  9. Example-5: Find the degree of Solution: The given differential equation is not a polynomial equation in So its degree is not defined. Note:By using power series expansion, sine function can be represented as So the expansion of will same as above but x will be replaced by . Now it is clearly visible that the degree of is increasing to infinity. That is , we can’t assign a specific value as degree of such kind of differential equation .

  10. Solution: The given differential equation is not a polynomial equation So its degree is not defined.

  11. What will be the degree of the differential equation when fractional powers cannot be eliminated? Solution: Least common multiple between 2, 3, 5=30 (1/5)⋅30=6 (1/2)⋅30=15 (2/3)⋅30=20 degree of the given differential equation =20 Max. degree

  12. Why is the degree of differential equation involving log, exponent and trigonometry functions not defined? In case of log, exponent, and trig functions; the highest power of sinusoidal(in case of trig), log and exponent goes to infinity. Hence the degree is not defined.

  13. Find the order and degree of the following differential equations:

More Related