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

The solution for (x+1)*(dy)/(dx)+y=ln(x) is y=(xln(x))/(x+1)-x/(x+1)+(c_{1})/(x+1)

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(x+1)*(dy)/(dx)+y=ln(x)

(x + 1) \cdot \frac{d y}{d x} + y = ln (x)

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

Solution steps

(x + 1) \cdot \frac{d y}{d x} + y = ln (x)

Solve linear ODE:

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

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

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

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