What is the solution for (dy}{dx}=\frac{x^2)/9+7/9 ?

The solution for (dy}{dx}=\frac{x^2)/9+7/9 is y=(x^3)/(27)+7/9 x+c_{1}

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(dy}{dx}=\frac{x^2)/9+7/9

\frac{d y}{d x} = \frac{x ^{2}}{9} + \frac{7}{9}

y = \frac{x ^{3}}{27} + \frac{7}{9} x + c_{1}

Solution steps

\frac{d y}{d x} = \frac{x ^{2}}{9} + \frac{7}{9}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{x ^{2}}{9} + \frac{7}{9}

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

then

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

y = \int \frac{x ^{2}}{9} + \frac{7}{9} d x

\int \frac{x ^{2}}{9} + \frac{7}{9} d x = \frac{x ^{3}}{27} + \frac{7}{9} x + c_{1}

y = \frac{x ^{3}}{27} + \frac{7}{9} x + c_{1}

What is the solution for (dy}{dx}=\frac{x^2)/9+7/9 ?
The solution for (dy}{dx}=\frac{x^2)/9+7/9 is y=(x^3)/(27)+7/9 x+c_{1}