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

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

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xln(x)(dy)/(dx)+y=xe^x

x ln (x) \frac{d y}{d x} + y = x e^{x}

y = \frac{e ^{x}}{ln ( x )} + \frac{c _{1}}{ln ( x )}

Solution steps

x ln (x) \frac{d y}{d x} + y = x e^{x}

Solve linear ODE:

y = \frac{e ^{x}}{ln ( x )} + \frac{c _{1}}{ln ( x )}

y = \frac{e ^{x}}{ln ( x )} + \frac{c _{1}}{ln ( x )}

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