I'm having trouble understanding this for some reason...am I right about these? xy' - 4y = 0 is linear. y' = y - x^3 is linear. x' + 2x - e^(-x) = 0 is non-linear.
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Originally Posted by euphony I'm having trouble understanding this for some reason...am I right about these? xy' - 4y = 0 is linear. y' = y - x^3 is linear. x' + 2x - e^(-x) = 0 is non-linear. An ODE is linear if it is of the form . Where is the nth derivative of y(x) and all the a(x), b(x), ...., c(x), F(x) are all functions of x only. -Dan
Note that in the first two you are thinking of "x" as the independent variable- y is a function of x. But in the last, x is the dependent variable- x is a function of some unnamed variable.
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