What is the solution for (1+3/y+x)(dy)/(dx)+y= 3/x-1 ?

The solution for (1+3/y+x)(dy)/(dx)+y= 3/x-1 is y=(3\W((x(x+1))/(3e^{\frac{x-c_{1))/3}})}{x+1}

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(1+3/y+x)(dy)/(dx)+y= 3/x-1

(1 + \frac{3}{y} + x) \frac{d y}{d x} + y = \frac{3}{x} - 1

y = \frac{3 W ( \frac{x ( x + 1 )}{3 e ^{\frac{x - c _{1}}{3}}} )}{x + 1}

Solution steps

(1 + \frac{3}{y} + x) \frac{d y}{d x} + y = \frac{3}{x} - 1

Solve exact ODE:

y = \frac{3 W ( \frac{x ( x + 1 )}{3 e ^{\frac{x - c _{1}}{3}}} )}{x + 1}

y = \frac{3 W ( \frac{x ( x + 1 )}{3 e ^{\frac{x - c _{1}}{3}}} )}{x + 1}

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What is the solution for (1+3/y+x)(dy)/(dx)+y= 3/x-1 ?
The solution for (1+3/y+x)(dy)/(dx)+y= 3/x-1 is y=(3\W((x(x+1))/(3e^{\frac{x-c_{1))/3}})}{x+1}