Question

State whether the given differential equations are linear or not. Give the order of each equation.

(a) (1-x)y''-4xy'+5y=cosx
(b) x d^3y/dx^3

Answer 1

The first given differential equation is non-linear due to the term (1-x)y'', and its order is second. The second equation lacks sufficient information for assessment.

Step-by-step explanation:

The question asks to determine if two given differential equations are linear and to specify their order.

1. The first equation (1-x)y'' - 4xy' + 5y = cosx is non-linear due to the term (1-x)y''. A linear differential equation does not have functions or products of the dependent variable and/or its derivatives. Furthermore, the order of this equation is second, as the highest derivative present is y'' (the second derivative of y with respect to x).
2. The second equation x d^3y/dx^3 lacks enough information to form a complete differential equation and to assess linearity.