It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involved) and whether or not the equation is linear .
Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear:

 ?   1st order Linear 2nd order Linear 3rd order Linear 4th order Linear 5th order Linear 1st order Nonlinear 2nd order Nonlinear 3rd order Nonlinear 4th order Nonlinear 5th order Nonlinear  1. $\displaystyle \frac{d^4y}{dt^4} +\frac{d^3y}{dt^3} +\frac{d^2y}{dt^2}+\frac{dy}{dt}=1$

 ?   1st order Linear 2nd order Linear 3rd order Linear 4th order Linear 5th order Linear 1st order Nonlinear 2nd order Nonlinear 3rd order Nonlinear 4th order Nonlinear 5th order Nonlinear  2. $\displaystyle \frac{dy}{dt}+ty^2=0$

 ?   1st order Linear 2nd order Linear 3rd order Linear 4th order Linear 5th order Linear 1st order Nonlinear 2nd order Nonlinear 3rd order Nonlinear 4th order Nonlinear 5th order Nonlinear  3. $y''-y+y^2=0$

 ?   1st order Linear 2nd order Linear 3rd order Linear 4th order Linear 5th order Linear 1st order Nonlinear 2nd order Nonlinear 3rd order Nonlinear 4th order Nonlinear 5th order Nonlinear  4. $y''-y+t^2 = 0$