Find the order and degree of the differential equation: .

Asked by Topperlearning User | 4th Nov, 2016, 07:15: AM

Expert Answer:

T h e space g i v e n space e q u a t i o n space i s
space y equals x fraction numerator d y over denominator d x end fraction plus square root of a squared open parentheses fraction numerator d y over denominator d x end fraction close parentheses squared plus b squared end root
rightwards double arrow space y minus x fraction numerator d y over denominator d x end fraction equals square root of a squared open parentheses fraction numerator d y over denominator d x end fraction close parentheses squared plus b squared end root
s q u a r i n g space o n space b o t h space s i d e s space w e space g e t
open parentheses space y minus x fraction numerator d y over denominator d x end fraction close parentheses squared equals a squared open parentheses fraction numerator d y over denominator d x end fraction close parentheses squared plus b squared
equals y squared plus x squared open parentheses fraction numerator d y over denominator d x end fraction close parentheses squared minus 2 x y fraction numerator d y over denominator d x end fraction equals a squared open parentheses fraction numerator d y over denominator d x end fraction close parentheses squared plus b squared
equals y squared plus open parentheses fraction numerator d y over denominator d x end fraction close parentheses squared left parenthesis x squared minus a squared right parenthesis minus 2 x y fraction numerator d y over denominator d x end fraction minus b squared equals 0
F r o m space t h e space a b o v e space e q u a t i o n space w e space c a n space s e e space t h a t space t h e space h i g h e s t space d e r i v a t i v e space t e r m space i s
fraction numerator d y over denominator d x end fraction space w i t h space h i g h e s t space p o w e r space o f space 2 space s o space t h e space g i v e n space d i f f e r e n t i a l space e q a u t i o n space h a s space o r d e r space 1 space a n d space d e g r e e space 2.

 

Answered by  | 4th Nov, 2016, 09:15: AM