What is the solution for xy^'-2y=-2x^2-x+1 ?

The solution for xy^'-2y=-2x^2-x+1 is y=-2x^2ln(x)+x-1/2+c_{1}x^2

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xy^'-2y=-2x^2-x+1

x y^{^{'}} - 2 y = - 2 x^{2} - x + 1

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d}{d x} ((2 x + 7)^{2})

\frac{d}{d x} y - y = 3

y = \frac{3}{x}, y = 8 x, y = \frac{1}{8} x

\frac{d}{d x} (x^{3} + 8 x)

\frac{1}{1 - x ^{2}}, 0

What is the solution for xy^'-2y=-2x^2-x+1 ?
The solution for xy^'-2y=-2x^2-x+1 is y=-2x^2ln(x)+x-1/2+c_{1}x^2