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Math Help - is there lenear euqation that..

  1. #1
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    is there lenear euqation that..

    doesnt have constant coefficients?
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  2. #2
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    Quote Originally Posted by transgalactic View Post
    doesnt have constant coefficients?
    Yes.

    As long as you have (for lack of a better term) a "polynomial DE" of the form

    f_n(x) \frac{d^ny}{dx^n} + f_{n - 1}(x) \frac{d^{n - 1}y}{dx^{n - 1}} + f_{n - 2}(x) \frac{d^{n - 2}y}{dx^{n - 2}} + \dots + f_2(x)\frac{d^2y}{dx^2} + f_1(x) \frac{dy}{dx} + f_0(x) y = f(x).


    In other words, as long as the coefficients are nothing more than functions of x, the equation is still linear.
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    can you give an example of some thing which is not a function of x?
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    E.g.

    x^2\frac{d^2y}{dx^2} + 3x^4\frac{dy}{dx} + 7xy = 8\sin{x}.


    Do you see that the coefficients are nothing more than functions of x?
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    can you give an example of non lenear equation?
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  6. #6
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    Quote Originally Posted by transgalactic View Post
    can you give an example of non lenear equation?
    \frac{d^2y}{dx^2} + 3x\sin{y}\frac{dy}{dx} + 6y = 0.


    Can you see how the coefficient of \frac{dy}{dx} is "more than" a function of x? It has a function of y in it as well.
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  7. #7
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    yes i understand thanks
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