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Math Help - Differential Equations - General Solutions

  1. #1
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    Differential Equations - General Solutions

    Hey there, wondering if you could help me with a quick question please?

    Okay this is the question:

    1. Find the General Solution of the Equation:

    \frac{x^2}{y^3} \frac{dx}{dy} = 3

    Answer in the form y=f(x)

    Any response muchly appreciated!
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Nick87 View Post
    Hey there, wondering if you could help me with a quick question please?

    Okay this is the question:

    1. Find the General Solution of the Equation:

    \frac{x^2}{y^3} \frac{dx}{dy} = 3

    Answer in the form y=f(x)

    Any response muchly appreciated!
    Multiplying both sides by y^3dy

    Gives us

    x^2dx=3y^3dy

    Integrating both sides gives

    \frac{x^3}{3}+C=\frac{3y^4}{4}

    solving for y gives

    \sqrt[4]{\frac{4}{3}\cdot\frac{x^3}{3}+C_1}=|y|
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  3. #3
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    Thanks, that helps alot!
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