What is the solution for ((dy))/((dx))=8x^{(3)}+6x^{(2)} ?

The solution for ((dy))/((dx))=8x^{(3)}+6x^{(2)} is y=2x^4+2x^3+c_{1}

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((dy))/((dx))=8x^{(3)}+6x^{(2)}

\frac{( d y )}{( d x )} = 8 x^{(3)} + 6 x^{(2)}

y = 2 x^{4} + 2 x^{3} + c_{1}

Solution steps

\frac{( d y )}{( d x )} = 8 x^{(3)} + 6 x^{(2)}

Let

y

be the dependent variable. Divide by

d x

\frac{\frac{d y}{d x}}{1} = 8 x^{3} + 6 x^{2}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

\frac{y ^{^{'}} ( x )}{1} = 8 x^{3} + 6 x^{2}

Isolate

y^{'} (x) : y^{'} (x) = 8 x^{3} + 6 x^{2}

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

then

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

y = \int 8 x^{3} + 6 x^{2} d x

\int 8 x^{3} + 6 x^{2} d x = 2 x^{4} + 2 x^{3} + c_{1}

y = 2 x^{4} + 2 x^{3} + c_{1}

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What is the solution for ((dy))/((dx))=8x^{(3)}+6x^{(2)} ?
The solution for ((dy))/((dx))=8x^{(3)}+6x^{(2)} is y=2x^4+2x^3+c_{1}