Linearity in differential equations

[Chris B]

Homework Statement

Is the equation
(x²sinx + 4y) dx + x dy=0
linear
This problem also asks me to solve it, but I don't have a problem with that part.

Homework Equations

An equation is linear if the function or its derivative are only raised to the first power and not multiplied by each other.

The Attempt at a Solution

The answer in the back of the book says that it's linear with x as the dependent variable. I tried rearranging so that all x's were to the first power, but nothing doing. Is it a typo and it meant it's linear with y as the dependent variable? Because y is already by itself, and if you divide by dx then y' and y aren't multiplied by each other either so
x²sinx + 4y =-x dy/dx

Right? Have I mixed up dependent and independent somehow?

 

[vela]

"The function" refers to y.

 

[Chris B]

"The function" refers to y.

Fair enough, but if y is the function then x is the independent variable, right?

 

[AfterSunShine]

Right.

 

[Chris B]

Okay, then my book's answer key is wrong. Thanks.

 

[AfterSunShine]

You are welcome.
But just to add :
" An equation is linear if the function or its derivative are only raised to the first power, not multiplied by each other and not composited with other function ."

i.e. there is no cos(y), ln(y) , arctan(y'), e^y .. etc