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The differential equation is $\"\\frac{dy}{dx}=2x^{-3}\"$ .

$\"{dy}=2x^{-3}{dx}\"$

Integrate on both sides.

$\"\\int$

$\"y=2\\int$

Power rule of integration: $\"\\int$ .

$\"y=2\\frac{x^{-3+1}}{-3+1}+C\"$

$\"=\\frac{2x^{-2}}{-2}+C\"$

$\"={-x^{-2}}+C\"$

The general solution of differential eqation is $\"y=\\frac{-1}{x^2}+C\"$ .

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Check the result by differentiation.

$\"y=\\frac{-1}{x^2}+C\"$

Apply derivative on each side with respect to $\"x\"$ .

$\"\\frac{d}{dx}y=\\frac{d}{dx}\\left$

$\"\\small$

$\"=\\frac{d}{dx}\\left$

$\"=\\frac{d}{dx}\\left$

$\"={-(-2)x^{-2-1}}\"$

$\"={2x^{-3}}\"$

$\"\\frac{dy}{dx}=\\frac{2}{x^3}\"$ .

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The general solution of differential equation is $\"y=\\frac{-1}{x^2}+C\"$ .