What is the solution for y^'=x^2(x-2)^2(x-1)^2 ?

The solution for y^'=x^2(x-2)^2(x-1)^2 is y=(x^7)/7-x^6+(13x^5)/5-3x^4+(4x^3)/3+c_{1}

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y^'=x^2(x-2)^2(x-1)^2

y^{^{'}} = x^{2} (x - 2)^{2} (x - 1)^{2}

y = \frac{x ^{7}}{7} - x^{6} + \frac{13 x ^{5}}{5} - 3 x^{4} + \frac{4 x ^{3}}{3} + c_{1}

Solution steps

y^{'} (x) = x^{2} (x - 2)^{2} (x - 1)^{2}

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

then

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

y = \int x^{2} (x - 2)^{2} (x - 1)^{2} d x

\int x^{2} (x - 2)^{2} (x - 1)^{2} d x = \frac{x ^{7}}{7} - x^{6} + \frac{13 x ^{5}}{5} - 3 x^{4} + \frac{4 x ^{3}}{3} + c_{1}

y = \frac{x ^{7}}{7} - x^{6} + \frac{13 x ^{5}}{5} - 3 x^{4} + \frac{4 x ^{3}}{3} + c_{1}

\int_{- 1}^{1} (3 x^{3} - x^{2} + x - 1) d x

x^{3} sin (7 x)

\frac{\partial}{\partial x} (sin (7 x + y + 3 z))

\frac{d}{d x} (6 + 7 x)

e^{3 x}, 0

What is the solution for y^'=x^2(x-2)^2(x-1)^2 ?
The solution for y^'=x^2(x-2)^2(x-1)^2 is y=(x^7)/7-x^6+(13x^5)/5-3x^4+(4x^3)/3+c_{1}