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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

(- 2, 0), (0, 1)

y^{^{'}} + \frac{3}{t ^{2}} y = 0

sin (6 (t - \frac{3 π}{6}))

\frac{d}{d x} (x (e^{- x}))

\frac{\partial}{\partial x} (\frac{x y}{e ^{x^{2} + y^{2}}})

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