What is the solution for x(dy)/(dx)+(2x+1)/(x+1)y=x-1 ?

The solution for x(dy)/(dx)+(2x+1)/(x+1)y=x-1 is y=(x^2)/(3(x+1))-1/(x+1)+(c_{1})/(x^2+x)

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x(dy)/(dx)+(2x+1)/(x+1)y=x-1

x \frac{d y}{d x} + \frac{2 x + 1}{x + 1} y = x - 1

y = \frac{x ^{2}}{3 ( x + 1 )} - \frac{1}{x + 1} + \frac{c _{1}}{x ^{2} + x}

Solution steps

x \frac{d y}{d x} + \frac{2 x + 1}{x + 1} y = x - 1

Solve linear ODE:

y = \frac{x ^{2}}{3 ( x + 1 )} - \frac{1}{x + 1} + \frac{c _{1}}{x ^{2} + x}

y = \frac{x ^{2}}{3 ( x + 1 )} - \frac{1}{x + 1} + \frac{c _{1}}{x ^{2} + x}

\frac{1}{1 - \frac{1}{x}}, 0

\int \frac{1}{( b ^{2} - x ^{2} ) ^{\frac{3}{2}}} d x

f (x) = 10 x^{2} + 10 x + 8 + ln (x)

y^{^{''}} + 9 y = cos (6 t)

x \to 2 - lim (2)

What is the solution for x(dy)/(dx)+(2x+1)/(x+1)y=x-1 ?
The solution for x(dy)/(dx)+(2x+1)/(x+1)y=x-1 is y=(x^2)/(3(x+1))-1/(x+1)+(c_{1})/(x^2+x)