What is the solution for (dy)/(dx)=(x-18)^2 ?

The solution for (dy)/(dx)=(x-18)^2 is y=(x^3)/3-18x^2+324x+c_{1}

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(dy)/(dx)=(x-18)^2

\frac{d y}{d x} = (x - 18)^{2}

y = \frac{x ^{3}}{3} - 18 x^{2} + 324 x + c_{1}

Solution steps

\frac{d y}{d x} = (x - 18)^{2}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = (x - 18)^{2}

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

then

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

y = \int (x - 18)^{2} d x

\int (x - 18)^{2} d x = \frac{x ^{3}}{3} - 18 x^{2} + 324 x + c_{1}

y = \frac{x ^{3}}{3} - 18 x^{2} + 324 x + c_{1}

What is the solution for (dy)/(dx)=(x-18)^2 ?
The solution for (dy)/(dx)=(x-18)^2 is y=(x^3)/3-18x^2+324x+c_{1}