What is the solution for (dy)/(dx)=5x(x-3) ?

The solution for (dy)/(dx)=5x(x-3) is y=5((x^3)/3-(3x^2)/2)+c_{1}

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(dy)/(dx)=5x(x-3)

\frac{d y}{d x} = 5 x (x - 3)

y = 5 (\frac{x ^{3}}{3} - \frac{3 x ^{2}}{2}) + c_{1}

Solution steps

\frac{d y}{d x} = 5 x (x - 3)

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 5 x (x - 3)

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

then

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

y = \int 5 x (x - 3) d x

\int 5 x (x - 3) d x = 5 (\frac{x ^{3}}{3} - \frac{3 x ^{2}}{2}) + c_{1}

y = 5 (\frac{x ^{3}}{3} - \frac{3 x ^{2}}{2}) + c_{1}

y^{^{'}} - y = 7 t e^{2 t}, y (0) = 1

e^{x} - 1

\frac{d}{d x} (\frac{1 - x}{1 + x})

\int \frac{4 x - 6}{x ^{2} + 4} d x

\int \frac{3}{2} x^{2} d x

What is the solution for (dy)/(dx)=5x(x-3) ?
The solution for (dy)/(dx)=5x(x-3) is y=5((x^3)/3-(3x^2)/2)+c_{1}