State the order of the given ordinary differential equation. (1 - x)y\" - 9xy\'

Question

State the order of the given ordinary differential equation. (1 - x)y" - 9xy' + 7y = cos x Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1. a_n(x) d^n y/dx^n + a_n - 1(x) d^n - 1 y/dx^n - 1 + ... + a_1 (x) dy/dx + a_0(x) y = g(x) linear nonlinear State the order of the given ordinary differential equation. t^7y^(5) - t^4y" + 6y = 0 Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1. a_n(x) d^n y/dx^n + a_n - 1(x) d^n - 1 y/dx^n - 1 + ... + a_1 (x) dy/dx + a_0(x) y = g(x) linear nonlinear

Explanation / Answer

1. It is a 2nd order differential equation becausethe highest derivative is y''.

Yes, it is a linear differential equation by comparing it with the given standard equation.

Here n = 2 (2nd order)

Here, a2x = (1-x) , a1x = -9x a0x = 7 g(x) = cosx

So, it is of the form of given differential equation.

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