What is the solution for (dy)/(dx)=(3ex-9e-x)^2 ?

The solution for (dy)/(dx)=(3ex-9e-x)^2 is y=3e^2x^3-27e^2x^2-2ex^3+9ex^2+(x^3)/3+81e^2x+c_{1}

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(dy)/(dx)=(3ex-9e-x)^2

\frac{d y}{d x} = (3 e x - 9 e - x)^{2}

y = 3 e^{2} x^{3} - 27 e^{2} x^{2} - 2 e x^{3} + 9 e x^{2} + \frac{x ^{3}}{3} + 81 e^{2} x + c_{1}

Solution steps

\frac{d y}{d x} = (3 e x - 9 e - x)^{2}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = (3 e x - 9 e - x)^{2}

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

then

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

y = \int (3 e x - 9 e - x)^{2} d x

\int (3 e x - 9 e - x)^{2} d x = 3 e^{2} x^{3} - 27 e^{2} x^{2} - 2 e x^{3} + 9 e x^{2} + \frac{x ^{3}}{3} + 81 e^{2} x + c_{1}

y = 3 e^{2} x^{3} - 27 e^{2} x^{2} - 2 e x^{3} + 9 e x^{2} + \frac{x ^{3}}{3} + 81 e^{2} x + c_{1}

\int_{1}^{2} \frac{7}{x ^{2}} d x

\frac{d y}{d x} = 3 x^{- 2} e^{- y}

\int \frac{( x ^{2} + 9 x + 1 )}{( x ^{2} + 1 ) ^{2}} d x

x^{2} y^{^{''}} + 4 x y^{^{'}} - 4 y = 0, y (1) = 0, y^{^{'}} (1) = 3

\int \frac{225}{x ^{3} - 15 x ^{2}} d x

What is the solution for (dy)/(dx)=(3ex-9e-x)^2 ?
The solution for (dy)/(dx)=(3ex-9e-x)^2 is y=3e^2x^3-27e^2x^2-2ex^3+9ex^2+(x^3)/3+81e^2x+c_{1}