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Math Help - Homogenous D.E. with Non-Constant Coefficients

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    Question Homogenous D.E. with Non-Constant Coefficients

    How do I go about solving this differential equation?

    I can't remember if we even covered this in my calculus class, but as soon as I see the solution it should jog my memory.

    0 = 4\frac{dy}{dx} + x\frac{d^{2}y}{(dx)^{2}} \quad \text{where} \quad y=f(x)

    Thanks again!
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    Re: Homogenous D.E. with Non-Constant Coefficients

    Since your ODE has no y, if you let \dfrac{dy}{dx} = u then \dfrac{d^2y}{dx^2} = \dfrac{d u}{d x} and substitute, your ODE will separate.
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    Re: Homogenous D.E. with Non-Constant Coefficients

    Quote Originally Posted by Danny View Post
    Since your ODE has no y, if you let \dfrac{dy}{dx} = u then \dfrac{d^2y}{dx^2} = \dfrac{d u}{d x} and substitute, your ODE will separate.
    And is also first-order linear...
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