Answer in Chemical Engineering for pavani #231348
March 11th, 2023
8)Solve (D²+3DD’+2D’^2)z=x cos y+e^x+y, Where D=∂∂x and D’=∂∂y.
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” , so the degree of this equation here is 1. See some more examples here:
- “dy/dx + 1 = 0,” degree is 1
- “(yu201du2019)^3 + 3yu201d + 6yu2019 u2013 12 = 0,” degree is 3
- “(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.
