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 y}{d t} + 8 t y = 5 t

\frac{d}{d x} (3 x + x^{2} - 3 x^{3} - x^{4})

arccsc (- 3 t^{2})

y = e^{- 5 x}

\frac{d}{d x} (x - 10 3 x)

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