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Math Help - Euler Equations

  1. #1
    Senior Member Danneedshelp's Avatar
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    Euler Equations

    Q: An equation of the form

    t^{2}\frac{d^{2}y}{dt^{2}}+\alpha\\t\frac{dy}{dt}+  \beta\\y=0, t>0 with \alpha and \beta real constants, is called an Euler equation.

    a) Let x=ln(t) and calculate \frac{d^{2}y}{dt^{2}} and \frac{dy}{dt} in terms of \frac{d^{2}y}{dx^{2}} and \frac{dy}{dx}.

    My question is, what funtion am I differentiating with respect x? Do I write y=t=e^{2} and differentiat that? What is the function y that I am differentiating?
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  2. #2
    MHF Contributor chisigma's Avatar
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    This problem has been 'attacked' and solved in...

    http://www.mathhelpforum.com/math-he...-question.html

    Kind regards

    \chi \sigma
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