Question #231348

8)Solve (D²+3DD'+2D'^2)z=x cos y+e^x+y, Where D=∂\∂x and D'=∂\∂y.


1
Expert's answer
2021-09-20T02:34:23-0400

The degree of the differential equation is the power of the highest order derivative, where the original equation is represented in the form of a polynomial equation in derivatives such as y’,y”, y”’, and so on.

(d2y/dx2)+2(dy/dx)+y=0(d2y/dx2)+ 2 (dy/dx)+y = 0 , so the degree of this equation here is 1. See some more examples here:

  • dy/dx+1=0,dy/dx + 1 = 0, degree is 1
  • (y”’)3+3y+6y’–12=0,(y”’)^3 + 3y” + 6y’ – 12 = 0, degree is 3
  • (dy/dx)+cos(dy/dx)=0;(dy/dx) + cos(dy/dx) = 0; it is not a polynomial equation in y′ and the degree of such a differential equation can not be defined.

Note:

Order and degree (if defined) of a differential equation are always positive integers.



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