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Thread: Differential equation solver

  1. #1
    Senior Member Vinod's Avatar
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    Differential equation solver

    Hello,
    How to solve $4*x^2*y" +12*x*y' +3*y=0, y(4)=\frac18, y'(4)=\frac{-3}{64}$ with the help of Droid48 calculator application? It involves stiff initial value problem as well as vector-value differential equation.
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  2. #2
    Member Walagaster's Avatar
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    Re: Differential equation solver

    Quote Originally Posted by Vinod View Post
    Hello,
    How to solve $4*x^2*y" +12*x*y' +3*y=0, y(4)=\frac18, y'(4)=\frac{-3}{64}$ with the help of Droid48 calculator application? It involves stiff initial value problem as well as vector-value differential equation.
    Try for a solution of the form $y=x^r$ and see what values of $r$ work. You shouldn't need a calculator for this.
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  3. #3
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    Re: Differential equation solver

    The Wronskian is going to be $Ce^{-\displaystyle \int \dfrac{3}{x}dx} = Ce^{-3\ln x} = e^{\ln x^{-3k}} = x^{-3k}$ for some constant $k$. So, as Walagaster says, the solution will be $x^r$ for some $r$.
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  4. #4
    Senior Member Vinod's Avatar
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    Re: Differential equation solver

    Quote Originally Posted by SlipEternal View Post
    The Wronskian is going to be $Ce^{-\displaystyle \int \dfrac{3}{x}dx} = Ce^{-3\ln x} = e^{\ln x^{-3k}} = x^{-3k}$ for some constant $k$. So, as Walagaster says, the solution will be $x^r$ for some $r$.
    Hello,
    How to compute wronskian? How it can be utilised to solve differential equations? Would you give me some more information of Wronskian. As far as i know it is a determinant that is related to linear independence of a set of differential equations.
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