What is the solution for 4xy^'=2xe^x-4y+6x^2 ?

The solution for 4xy^'=2xe^x-4y+6x^2 is y=(e^xx-e^x}{2x}+\frac{x^2)/2+(c_{1})/x

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4xy^'=2xe^x-4y+6x^2

4 x y^{^{'}} = 2 x e^{x} - 4 y + 6 x^{2}

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

Solution steps

4 x y^{'} (x) = 2 x e^{x} - 4 y + 6 x^{2}

Solve linear ODE:

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

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

\int x sin^{3} (x^{2}) cos (x^{2}) d x

\frac{d y}{d x} = x, y (11) = 5

y = 5 sec (x), at x = \frac{π}{3}

\frac{d}{d x} (- 5 e^{- 4 x})

\int_{0}^{2} (x + 1) d x

What is the solution for 4xy^'=2xe^x-4y+6x^2 ?
The solution for 4xy^'=2xe^x-4y+6x^2 is y=(e^xx-e^x}{2x}+\frac{x^2)/2+(c_{1})/x