Mathematics, 28.01.2020 05:31 carjsan5656
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
you have 10 choices to choose for each problem:
a. 1st. order linear differential equation
b. 2nd. order linear differential equation
c. 3rd. order linear differential equation
d. 4th. order linear differential equation
e. 5th. order linear differential equation
f. 1st. order non-linear differential equation
g. 2nd. order non-linear differential equation
h. 3rd. order non-linear differential equation
i. 4th. order non-linear differential equation
f. 5th. order non-linear differential equation
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