Is the First-Order Differential Equation Linear in Its Dependent Variable?

[pupeye11]

Homework Statement

Determine whether the given first-order differential equation is linear in the indicated dependent variable by matching it with the first differential equations given in #7.

Homework Equations

#7 $$(sin \theta)y^{'''} - (cos \theta)y^{'} = 2$$

#10 $$(u)dv + (v+uv-ue^u)du = 0;$$ in v; in u

The Attempt at a Solution

How can I do this problem when there is not a variable y in number 10?

 

[Mark44]

Homework Statement

Determine whether the given first-order differential equation is linear in the indicated dependent variable by matching it with the first differential equations given in #7.

Homework Equations

#7 $$(sin \theta)y^{'''} - (cos \theta)y^{'} = 2$$

Underline added below.

#10 $$(u)dv + (v+uv-ue^u)du = 0;$$ in v; in u

The Attempt at a Solution

How can I do this problem when there is not a variable y in number 10?

There does not need to be a variable y. In #10 the question is in two parts: Is the differential equation linear in the indicated dependent variable - in v, and then in u. For the first part, assume that v is the dependent variable; for the second part, assume that u is the independent variable.