What is the solution for x(dy)/(dx)+xy=1-y,y(1)=0 ?

The solution for x(dy)/(dx)+xy=1-y,y(1)=0 is y= 1/x-(e^{1-x})/x

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x(dy)/(dx)+xy=1-y,y(1)=0

x \frac{d y}{d x} + x y = 1 - y, y (1) = 0

y = \frac{1}{x} - \frac{e ^{1 - x}}{x}

Solution steps

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

Solve linear ODE:

y = \frac{1}{x} - \frac{e ^{1 - x}}{x}

y = \frac{1}{x} - \frac{e ^{1 - x}}{x}

(e^{x} + y) d x + (2 + x + y e^{y}) d y = 0, y (0) = 0

y = x^{3}, y = x^{2}, x = - 1

\int \frac{23}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

x \to 5 - lim (\frac{8 x}{x - 5})

\frac{d}{d t} (b sin (t))

What is the solution for x(dy)/(dx)+xy=1-y,y(1)=0 ?
The solution for x(dy)/(dx)+xy=1-y,y(1)=0 is y= 1/x-(e^{1-x})/x