cannot be expressed as polynomial equation with d y as the leading term So, the degree of the equation is not defined. The order of the equation is . ( ) Further, the following differential equations do not have degrees. (i) e dx + = (ii) log d y + and (iii) cos d y d y + ( ) The differential equation sin( ′′′ ′′ ′ + has order but degree is not defined.
( ) The differential equation cos( ′ ′′′+ ′′+ ′ = y y has order and degree is not defined. Remark Observe that the degree of a differential equation is always a positive integer. Example . Determine the order and degree (if exists) of the following differential equations: (i) dy + (ii) d y + + = cos (iii) d y d y + = (iv) d y = + (v) dy - - (i) In this equation, the highest order derivative is dy dx whose power is Therefore, the given differential equation is of order and degree .
(ii) Here, the highest order derivative is d y whose power is . Therefore, the given differential equation is of order and degree . (iii) In the given differential equation, the highest order derivative is d y whose power is . Therefore, the given differential equation is of order .
The given differential equation is not a polynomial equation in its derivatives and so its degree is not defined. (iv) The given differential equation is d y = + Squaring both sides, we get d y = + In this equation, the highest order derivative is d y whose power is . Therefore, the given differential equation is of order and degree . (v) dy is a first order differential equation with degree , since