It can be to classify a differential equation, so that we can predict the techniques that might 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:
1. (1+y2)(d2y/dt2)+t(dy/dt)+y=et
2. t2(d2y/dt2)+t(dy/dt)+2y=sin t
3. (d3y/dt3)+t(dy/dt)+(cos2(t))y=t3
4. y''-y+y2=0

Step-by-step explanation:

The objective is to determine whether or not each of the following equation is linear:

We can rewrite this equation in the form

                      .

As we can see, this is an second-order nonlinear differential equation, because of the term next to .

We can rewrite this equation in the form

                         .

This is an second-order linear ordinary differential equation.

We can rewrite this equation in the form

This is an third-order linear ordinary differential equation.

This is an second-order nonlinear ordinary differential equation, because of the term .

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.