What is the solution for 6xy^'=2xe^x-6y+6x^2 ?

The solution for 6xy^'=2xe^x-6y+6x^2 is y=(e^xx-e^x}{3x}+\frac{x^2)/3+(c_{1})/x

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6xy^'=2xe^x-6y+6x^2

6 x y^{^{'}} = 2 x e^{x} - 6 y + 6 x^{2}

y = \frac{e ^{x} x - e ^{x}}{3 x} + \frac{x ^{2}}{3} + \frac{c _{1}}{x}

Solution steps

6 x y^{'} (x) = 2 x e^{x} - 6 y + 6 x^{2}

Solve linear ODE:

y = \frac{e ^{x} x - e ^{x}}{3 x} + \frac{x ^{2}}{3} + \frac{c _{1}}{x}

y = \frac{e ^{x} x - e ^{x}}{3 x} + \frac{x ^{2}}{3} + \frac{c _{1}}{x}

\frac{\partial}{\partial v} (u^{2})

\int \frac{1}{2 k ^{2}} \cdot e^{- \frac{x}{2 k ^{2}}} d x

\int \frac{1 - u}{1 + u ^{2}} d u

\int x^{2} (x^{3} + 5)^{8} cos ((x^{3} + 5)^{9}) d x

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

What is the solution for 6xy^'=2xe^x-6y+6x^2 ?
The solution for 6xy^'=2xe^x-6y+6x^2 is y=(e^xx-e^x}{3x}+\frac{x^2)/3+(c_{1})/x