`=>` To study the degree of a differential equation, the key point is that the differential equation must be a polynomial equation in derivatives, i.e., y′, y″, y″′ etc.
Consider the following differential equations:
`color{orange} {(d^3y)/(dx^3) + 2 ((d^2y)/(dx^2))^2 - (dy)/(dx) + y = 0}` .......(9)
`color{orange} {((dy)/(dx))^2 + ((dy)/(dx)) - sin^2 y = 0}`.......(10)
`color{orange} {(dy)/(dx) + sin ((dy)/(dx)) = 0}` .........(11)
`=>` By the degree of a differential equation, when it is a polynomial equation in derivatives, we mean the highest power (positive integral index) of the highest order derivative involved in the given differential equation.
`=>` In view of the above definition, one may observe that differential equations (6), (7), (8) and (9) each are of degree one, equation (10) is of degree two while the degree of differential equation (11) is not defined.
Note : Order and degree (if defined) of a differential equation are always positive integers.
`=>` To study the degree of a differential equation, the key point is that the differential equation must be a polynomial equation in derivatives, i.e., y′, y″, y″′ etc.
Consider the following differential equations:
`color{orange} {(d^3y)/(dx^3) + 2 ((d^2y)/(dx^2))^2 - (dy)/(dx) + y = 0}` .......(9)
`color{orange} {((dy)/(dx))^2 + ((dy)/(dx)) - sin^2 y = 0}`.......(10)
`color{orange} {(dy)/(dx) + sin ((dy)/(dx)) = 0}` .........(11)
`=>` By the degree of a differential equation, when it is a polynomial equation in derivatives, we mean the highest power (positive integral index) of the highest order derivative involved in the given differential equation.
`=>` In view of the above definition, one may observe that differential equations (6), (7), (8) and (9) each are of degree one, equation (10) is of degree two while the degree of differential equation (11) is not defined.
Note : Order and degree (if defined) of a differential equation are always positive integers.