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Find the general solution of the differential equations `x^5(dy)/(dx)=-y^5`

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To solve the differential equation \( x^5 \frac{dy}{dx} = -y^5 \), we will follow these steps: ### Step 1: Rearranging the Equation We start by rearranging the equation to separate the variables \( y \) and \( x \). \[ \frac{dy}{dx} = -\frac{y^5}{x^5} \] ...
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Knowledge Check

  • Find the general solution of the differential equation y-x(dy)/(dx)=a(y^(2)+(dy)/(dx)) .

    A
    `y=C(1-ay)(a+x)`
    B
    `y=C(1+ay)(a+x)`
    C
    `y=C(a+x)`
    D
    `y=C(1-ay)`

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