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The differential equation is $\"\\frac{dy}{dt}=9t^2\"$ .

$\"{dy}=9t^2$

Apply integral on each side.

$\"\\int$

$\"y=9\\int$

Apply power rule of integration $\"\\int$ .

$\"y=9\\frac{t^{2+1}}{2+1}+C\"$

$\"y=\\frac{9t^{3}}{3}+C\"$

The general solution of differential equation is $\"y={3t^{3}}+C\"$ .

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Check:

$\"y={3t^{3}}+C\"$

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

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

$\"\\frac{dy}{dt}=\\left$

$\"\\frac{dy}{dt}=9t^{2}}\"$ .

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The general solution of differential equation is $\"y={3t^{3}}+C\"$ .