What is the solution for (y-b)*y^'+x-a=0 ?

The solution for (y-b)*y^'+x-a=0 is y=b+sqrt(-x^2+2ax+c_{1)+b^2},y=b-sqrt(-x^2+2ax+c_{1)+b^2}

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(y-b)*y^'+x-a=0

(y - b) \cdot y^{^{'}} + x - a = 0

y = b + - x^{2} + 2 a x + c_{1} + b^{2}, y = b - - x^{2} + 2 a x + c_{1} + b^{2}

Solution steps

(y - b) \cdot y^{'} (x) + x - a = 0

Solve separable ODE:

y = b + - x^{2} + 2 a x + c_{1} + b^{2}, y = b - - x^{2} + 2 a x + c_{1} + b^{2}

y = b + - x^{2} + 2 a x + c_{1} + b^{2}, y = b - - x^{2} + 2 a x + c_{1} + b^{2}

What is the solution for (y-b)*y^'+x-a=0 ?
The solution for (y-b)*y^'+x-a=0 is y=b+sqrt(-x^2+2ax+c_{1)+b^2},y=b-sqrt(-x^2+2ax+c_{1)+b^2}