What is the solution for (dy)/(dx)-y/x =xe^x,y(1)=e-1 ?

The solution for (dy)/(dx)-y/x =xe^x,y(1)=e-1 is y=e^xx-x

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(dy)/(dx)-y/x =xe^x,y(1)=e-1

\frac{d y}{d x} - \frac{y}{x} = x e^{x}, y (1) = e - 1

y = e^{x} x - x

Solution steps

\frac{d y}{d x} - \frac{y}{x} = x e^{x}

Solve linear ODE:

y = e^{x} x - x

y = e^{x} x - x

x \to \infty lim (\frac{1}{4 x})

\int_{- 1}^{5} (1 + 3 x) d x

\frac{d y}{d x} = \frac{x}{- y}

y = arcsin (2 x + 1)

\frac{d}{d x} (e^{9 x})

What is the solution for (dy)/(dx)-y/x =xe^x,y(1)=e-1 ?
The solution for (dy)/(dx)-y/x =xe^x,y(1)=e-1 is y=e^xx-x