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 .

all it means is function 3

answer: 177/8

step-by-step explanation: