What is the solution for (x+1)(dy)/(dx)+y=ln(x),y(1)=15 ?

The solution for (x+1)(dy)/(dx)+y=ln(x),y(1)=15 is y=(xln(x))/(x+1)-x/(x+1)+(31)/(x+1)

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(x+1)(dy)/(dx)+y=ln(x),y(1)=15

(x + 1) \frac{d y}{d x} + y = ln (x), y (1) = 15

y = \frac{x ln ( x )}{x + 1} - \frac{x}{x + 1} + \frac{31}{x + 1}

Solution steps

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

Solve linear ODE:

y = \frac{x ln ( x )}{x + 1} - \frac{x}{x + 1} + \frac{31}{x + 1}

y = \frac{x ln ( x )}{x + 1} - \frac{x}{x + 1} + \frac{31}{x + 1}

\frac{x ^{2} - 1}{x ^{2} + 4}

\int \frac{ln ( x + 4 )}{x + 4} d x

\int (sec (y) tan (y) - csc (y) cot (y)) d y

y = 1 + 5 x, 1 \leq x \leq 7

What is the solution for (x+1)(dy)/(dx)+y=ln(x),y(1)=15 ?
The solution for (x+1)(dy)/(dx)+y=ln(x),y(1)=15 is y=(xln(x))/(x+1)-x/(x+1)+(31)/(x+1)