What is the solution for y^'=12t^5-20t^4+2-6t^{-2} ?

The solution for y^'=12t^5-20t^4+2-6t^{-2} is y=2t^6-4t^5+2t+6/t+c_{1}

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y^'=12t^5-20t^4+2-6t^{-2}

y^{^{'}} = 12 t^{5} - 20 t^{4} + 2 - 6 t^{- 2}

y = 2 t^{6} - 4 t^{5} + 2 t + \frac{6}{t} + c_{1}

Solution steps

y^{'} (t) = 12 t^{5} - 20 t^{4} + 2 - 6 t^{- 2}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int 12 t^{5} - 20 t^{4} + 2 - 6 t^{- 2} d t

\int 12 t^{5} - 20 t^{4} + 2 - 6 t^{- 2} d t = 2 t^{6} - 4 t^{5} + 2 t + \frac{6}{t} + c_{1}

y = 2 t^{6} - 4 t^{5} + 2 t + \frac{6}{t} + c_{1}

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What is the solution for y^'=12t^5-20t^4+2-6t^{-2} ?
The solution for y^'=12t^5-20t^4+2-6t^{-2} is y=2t^6-4t^5+2t+6/t+c_{1}