It can be helpful to classify a differential equation, so that we can predict th

Question

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: d^4 y/dt^4 + d^3 y/dt^3 + d^2 y/dt^2 + dy/dt = 1 y" - y + y^2 = 0 d^2 y/dt^2 + sin (t + y) = sin t dy/dt + ty^2 = 0

Explanation / Answer

Linear just means that the variable in an equation appears only with a power of one. So y is linear but y2 is non-linear. Also any function like cos(y) is non-linear. linear generally means "simple" and non-linear means "complicated".

Answer of the fourth differential equation is :

" First order = Since number of highest derivative is 1"

" Non Liner= because y^2 is not a first power

thus our answer is First order,Non linear.

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