What is the solution for (dy)/(dx)(x+1)+y=ln(x),y(1)=10 ?

The solution for (dy)/(dx)(x+1)+y=ln(x),y(1)=10 is y=(xln(x))/(x+1)-x/(x+1)+(21)/(x+1)

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(dy)/(dx)(x+1)+y=ln(x),y(1)=10

\frac{d y}{d x} (x + 1) + y = ln (x), y (1) = 10

y = \frac{x ln ( x )}{x + 1} - \frac{x}{x + 1} + \frac{21}{x + 1}

Solution steps

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

Solve linear ODE:

y = \frac{x ln ( x )}{x + 1} - \frac{x}{x + 1} + \frac{21}{x + 1}

y = \frac{x ln ( x )}{x + 1} - \frac{x}{x + 1} + \frac{21}{x + 1}

2 x^{2}, (3, 18)

x^{2} y^{^{''}} + 4 x y^{^{'}} + 2 y = \frac{1}{x}

3 \frac{d y}{d x} + \frac{8}{x y ^{2}} = 0

\frac{d}{d x} (\frac{2}{x + 5})

x \to 0 + lim (cot (x) - csc (x))

What is the solution for (dy)/(dx)(x+1)+y=ln(x),y(1)=10 ?
The solution for (dy)/(dx)(x+1)+y=ln(x),y(1)=10 is y=(xln(x))/(x+1)-x/(x+1)+(21)/(x+1)