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} (e^{2 x} + e^{- 3 x})

t an g e n t y = arccos (x) + x

7 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 7 x e^{- y}

t^{2} y^{^{''}} + 4 t y^{^{'}} - 18 y = 0

\frac{\partial}{\partial x} (- 2 x e^{- 3 x y})

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