Question

how would you know if it is a linear differential equation or not?

Answer 1

when the dy and the dx part are raised to the power of 0 or 1.
e.g \[dy/dx\]
anything with the above is linear.But
\[d^2y/dx^2\] is second order differential equation because the dependant variables dy and dx are raised to the power of 2.

Answer 2

so it depends on the power? what about if there are trigonometric functions?

Answer 3

yes we only look at the dy and the dx. It does not matter if they are trigonometric functions raised to the power of any number.You determine the linearity by looking at the powers on dy and dx.