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

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

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

\frac{x 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

\frac{x 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}

\frac{\partial}{\partial x} (5 x^{3} + 4 x y^{3})

\int \frac{x ^{2} + 1}{x} d x

n = 1 \sum \infty \frac{x ^{n - 1}}{x}

x \to 1 lim (- 1 x^{- 1 - 1} sin (\frac{1}{x}) - x^{- 1 - 2} cos (\frac{1}{x}))

2 t + 3

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