What is the solution for x*(dy)/(dx)=2xe^x-y+6x^2 ?

The solution for x*(dy)/(dx)=2xe^x-y+6x^2 is y=(2(e^xx-e^x))/x+2x^2+(c_{1})/x

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x*(dy)/(dx)=2xe^x-y+6x^2

x \cdot \frac{d y}{d x} = 2 x e^{x} - y + 6 x^{2}

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

Solution steps

x \cdot \frac{d y}{d x} = 2 x e^{x} - y + 6 x^{2}

Solve linear ODE:

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

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

\frac{d}{d y} (- x y sin (x) + 2 y cos (x))

y^{^{''}} + y = tan^{2} (x)

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

f (x) = \frac{x ^{2} + 5 x + 6}{x ^{2} - 4}

\int \frac{x}{x ^{4} - 1} d x

What is the solution for x*(dy)/(dx)=2xe^x-y+6x^2 ?
The solution for x*(dy)/(dx)=2xe^x-y+6x^2 is y=(2(e^xx-e^x))/x+2x^2+(c_{1})/x