What is the solution for (dy)/(dx)=4x(x-1) ?

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

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(dy)/(dx)=4x(x-1)

\frac{d y}{d x} = 4 x (x - 1)

y = 4 (\frac{x ^{3}}{3} - \frac{x ^{2}}{2}) + c_{1}

Solution steps

\frac{d y}{d x} = 4 x (x - 1)

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 4 x (x - 1)

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

then

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

y = \int 4 x (x - 1) d x

\int 4 x (x - 1) d x = 4 (\frac{x ^{3}}{3} - \frac{x ^{2}}{2}) + c_{1}

y = 4 (\frac{x ^{3}}{3} - \frac{x ^{2}}{2}) + c_{1}

\int_{0}^{1} (x 1 - x^{2}) d x

f (x) = e^{2 x - 5} + 4

y^{^{'}} = \frac{y ^{2} + 3 x x ^{2} + y ^{2}}{x y}

\int x (x + 1)^{6} d x

\int (\frac{x}{x ^{2} - 2}) d x

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