A Note Order and degree (if defined) of a differential equation are always positive integers. Example Find the order and degree, if defined, of each of the following differential equations: (i) dx − (ii) (iii) e ′ ′′′ + Solution (i) The highest order derivative present in the differential equation is dy dx , so its order is one. It is a polynomial equation in y ′ and the highest power raised to dy is one, so its degree is one. (ii) The highest order derivative present in the given differential equation is , so its order is two.
It is a polynomial equation in and dy dx and the highest power raised to is one, so its degree is one. (iii) The highest order derivative present in the differential equation is y ′′′ , so its order is three. The given differential equation is not a polynomial equation in its derivatives and so its degree is not defined. EXERCISE .
Determine order and degree (if defined) of differential equations given in Exercises to . . sin( ′′′ . y ′ + y = .
ds d s s dt dt + . . cos3 sin3 . y ′′′ + ( y ″ ) + ( y ′ ) + y = .
y ′′′ + y ″ + y ′ = . y ′ + y = e x . y ″ + ( y ′ ) + y = . y ″ + y ′ + sin y = .
The degree of the differential equation + = is (A) (B) (C) (D) not defined . The order of the differential equation is (A) (B) (C) (D) not defined . . General and Particular Solutions of a Differential Equation In earlier Classes, we have solved the equations of the type: x + = sin x – cos x = Solution of equations ( ) and ( ) are numbers, real or complex,