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

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

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

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

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

Solution steps

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

Solve Bernoulli ODE:

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

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

100 x^{2} + 400 x + 5000, 0.5

\int e^{y (1 - x)} d x

\frac{d}{d x} y = 7 x^{2} cos (x) cot (x)

\frac{d y}{d x} + e^{x} y = - 9 e^{x}

f (x) = \frac{6 x}{x - 1}, (- 1, 3)

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