Solve: dy/dx = 7/y2



{eq}\frac{dy}{dx} = \frac{7}{y^2} {/eq}

Differential Equations:

The differential equation would be an expression that contains both the variables and their corresponding differential terms. These equations can be solved through different methods, which would depend on their form. One method of solving differential equations is through the separation of variables.

Answer and Explanation:

Determine the general expression for the solution of the differential equation. We do this with the process of separation of variables, wherein we isolate the variables to either side of the equation and then integrate them. We proceed with the solution.

{eq}\begin{align} \displaystyle \frac{dy}{dx} &= \frac{7}{y^2} \\[0.3cm] y^2 dy &= 7dx \\[0.3cm] \int y^2 dy &= \int 7 dx \\[0.3cm] \frac{y^3}{3} &= 7x +C \\[0.3cm] y^3 &= 21x +C' \\[0.3cm] y &= \sqrt[3]{21x + C'} \end{align} {/eq}

Therefore, the general solution is expressed as {eq}\displaystyle \boxed{y(x) = \sqrt[3]{21x + C'}} {/eq}.

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