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Math Help - Differential Equation (iii)

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    Differential Equation (iii)

    I'm doing something wrong, could someone point me to the right direction...

    Find the general solution of the differential equation.

    x\frac{dy}{dx}-3y=x^{4}
    ANSWER: y=x^{3}(x+c)

    ---

    x\frac{dy}{dx}-3y=x^{4}

    -3y=x^{4}-x\frac{dy}{dx}

    3y=x\frac{dy}{dx}-x^{4}

    \frac{3y}{dy}=\frac{x}{dx}-x^{4}

    \int{\frac{3y}{dy}}=\int{\frac{x}{dx}}-\int{x^{4}}

    \frac{3}{2}y^{2}=\frac{1}{2}x^{2}-\frac{1}{5}x^{5}+c

    ...
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    Hello,

    Quote Originally Posted by r_maths View Post
    I'm doing something wrong, could someone point me to the right direction...

    Find the general solution of the differential equation.

    x\frac{dy}{dx}-3y=x^{4}
    ANSWER: y=x^{3}(x+c)

    ---

    x\frac{dy}{dx}-3y=x^{4}

    -3y=x^{4}-x\frac{dy}{dx}

    3y=x\frac{dy}{dx}-x^{4}

    \frac{3y}{dy}=\frac{x}{dx}-x^{4} SiMoon says : why didn't you divide x^4 by dy ?

    \int{\frac{3y}{dy}}=\int{\frac{x}{dx}}-\int{x^{4}}

    SiMoon says : these two last integrals make no sense, you don't know how to integrate when dx or dy is in the denominator

    \frac{3}{2}y^{2}=\frac{1}{2}x^{2}-\frac{1}{5}x^{5}+c

    ...
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    How do you divide x^4 by dy?
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    Quote Originally Posted by r_maths View Post
    I'm doing something wrong, could someone point me to the right direction...

    Find the general solution of the differential equation.

    x\frac{dy}{dx}-3y=x^{4}
    ANSWER: y=x^{3}(x+c)

    ---

    x\frac{dy}{dx}-3y=x^{4}

    -3y=x^{4}-x\frac{dy}{dx}

    3y=x\frac{dy}{dx}-x^{4}

    \frac{3y}{dy}=\frac{x}{dx}-x^{4}

    \int{\frac{3y}{dy}}=\int{\frac{x}{dx}}-\int{x^{4}}

    \frac{3}{2}y^{2}=\frac{1}{2}x^{2}-\frac{1}{5}x^{5}+c

    ...
    x\frac{dy}{dx}-3y=x^{4} \Rightarrow \frac{dy}{dx} - \frac{3}{x} y = x^{3}.

    The integrating factor technique is required.

    Note: The integrating factor is e^{\int -\frac{3}{x} \, dx} = e^{-3 \ln |x|} = e^{\ln |x|^{-3}} = \frac{1}{x^3}.
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    Moo
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    Quote Originally Posted by r_maths View Post
    How do you divide x^4 by dy?
    You divided it in one term only, which is not logical
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