What is the solution for x(dy)/(dx)=3xe^x-y+6x^2 ?

The solution for x(dy)/(dx)=3xe^x-y+6x^2 is y=(3(e^xx-e^x))/x+2x^2+(c_{1})/x

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x(dy)/(dx)=3xe^x-y+6x^2

x \frac{d y}{d x} = 3 x e^{x} - y + 6 x^{2}

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

Solution steps

x \frac{d y}{d x} = 3 x e^{x} - y + 6 x^{2}

Solve linear ODE:

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

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

x \to 1 lim (x^{\frac{4}{1 - x}})

\int - x^{2} + 25 d x

y^{^{''}} + 3 y^{^{'}} - 40 y = 0

\int \frac{- 2}{t + 1} d t

\frac{1200}{s ^{2} ( s + 10 ) ^{2}}

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