What is the solution for (dy)/(dx)+y/x =e^x ?

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

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(dy)/(dx)+y/x =e^x

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d}{d x} (d - b + \frac{- a x ^{3} - d}{x ^{2}})

\frac{d}{d x} (e^{2 x} + e^{- 3 x})

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

x \to 0 lim ((1 + x^{2})^{\frac{1}{x}})

4 \frac{d ^{2} x}{d t ^{2}} + 7 \frac{d x}{d t} + 15 x = 0

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