Determine the order the independent and dependent variables

Determine the order, the independent and dependent variables, and decide if the differential equation is linear.

Solution

Order - The order of a differential equation is the order of the highest derivative included in the equation. :

independent variable -   When a differential equation involves one or more derivatives with respect to a particular variable,   that variable is called the independent variable.

dependent variable =-   A variable is called dependent if a derivative of that variable occurs.

linear differential equation =   A linear differential equation is one in which the dependent variable only appears with an exponent of 0 or 1. (Note that the independent variable can appear raised to any power or as the argument of any function); it\'s only the exponent of the dependent variable that counts.

now

1) order - 2

independent variable - t

dependent variable - y

linear - no { because of y^0.5 term}

2)

order - 2

independent variable - s

dependent variable - t

linear -   no { because of s² term }

3)

order - 1

independent variable - y

dependent variable - x

linear - no {because of x² term}

4)

order - 3

independent variable - t

dependent variable - x

linear - yes

5)

order - 3

independent variable - x

dependent variable - y

linear - yes