Question

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

Explain the problem with step by step process?

Answer 1

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
• $(y”’)^3 + 3y” + 6y’ – 12 = 0,$ 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.