What is the solution for (y-x)y^'=y-x+3 ?

The solution for (y-x)y^'=y-x+3 is y=(2x+sqrt(24x+c_{1)})/2 ,y=(2x-sqrt(24x+c_{1)})/2

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(y-x)y^'=y-x+3

(y - x) y^{^{'}} = y - x + 3

y = \frac{2 x + 24 x + c _{1}}{2}, y = \frac{2 x - 24 x + c _{1}}{2}

Solution steps

(y - x) y^{'} (x) = y - x + 3

Solve exact ODE:

y = \frac{2 x + 24 x + c _{1}}{2}, y = \frac{2 x - 24 x + c _{1}}{2}

y = \frac{2 x + 24 x + c _{1}}{2}, y = \frac{2 x - 24 x + c _{1}}{2}

\int \frac{1}{1 + w ^{2}} d w

\frac{d}{d x} (2 1 + x^{2} + 1)

x \to 3 lim (ln (x^{2} - 9))

\int \frac{5 x ^{2} + 20 x + 6}{x ( x + 1 ) ^{2}} d x

\int x (2 x - 3) d x

What is the solution for (y-x)y^'=y-x+3 ?
The solution for (y-x)y^'=y-x+3 is y=(2x+sqrt(24x+c_{1)})/2 ,y=(2x-sqrt(24x+c_{1)})/2