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State the order of the given ordinary differential equation.

(1 − x)y'' − 7xy' + 5y = cos x


Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1.

Verified Answer :

wizard123

2nd Order because it contains a 2nd derivative ,y''

Linear because the y term is linear, in other words the y has no exponent, nor is it inside of a log or trig function.
ex:
ln(y) or sin(y) or e^y

The order of the given ordinary differential equation.

(1 − x)y'' − 7xy' + 5y = cos x is 2nd Order.

2nd Order because it is 2nd derivative function.

What is differential equation ?

Differential equations refers to the study of their solutions means the set of functions that satisfy each equation and the properties of their solutions.

Given : (1 − x)y'' − 7xy' + 5y = cos x

Here, according to the given differential equation is Linear  In other words the y has neither Exponent  nor is inside of a logarithmic or Trigonometric function.

For example:-   \(\rm log(y) or\; sin(y) \;or\; e^y\)

Therefore, The order of the given ordinary differential equation.

(1 − x)y'' − 7xy' + 5y = cos x is 2nd Order.

Learn more about Differential equations here: https://brainly.com/question/16967726

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