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Math Help - Differetial Equation with Sine Integral

  1. #1
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    Differetial Equation with Sine Integral

    Si(x)=integral(sint/tdt) from 0 to x
    integrand is 1 at t=0

    express the solution y(x) of the initial value problem x^3y'+2x^2y=10sinx, y(0)=0 in terms of Si(x).


    What I have done:
    y'+2/xy=10x^-3sinx
    multiply by x^2
    x^2y'+2xy=10x^-2sinx
    (x^2y)'=10x^-2sinx
    Now I get stuck because I feel like this can't be integrated and I don't think i can just insert Si(x) because I need to account for 10x^-2.
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  2. #2
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    Quote Originally Posted by kathrynmath View Post
    Si(x)=integral(sint/tdt) from 0 to x
    integrand is 1 at t=0

    express the solution y(x) of the initial value problem x^3y'+2x^2y=10sinx, y(0)=0 in terms of Si(x).


    What I have done:
    y'+2/xy=10x^-3sinx
    multiply by x^2
    x^2y'+2xy=10x^-2sinx
    (x^2y)'=10x^-2sinx
    Now I get stuck because I feel like this can't be integrated and I don't think i can just insert Si(x) because I need to account for 10x^-2.
    x^3y' + 2x^2y = 10\sin{x}

    x^2y' + 2xy = 10\cdot \frac{\sin{x}}{x}

    \frac{d}{dx}(x^2y) = 10\cdot\frac{\sin{x}}{x}

    x^2y = 10\int{\frac{\sin{x}}{x}\,dx}...


    Can you go from here?
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  3. #3
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    y=10x^(-2)Si(x)
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