What is the solution for (dy)/(dx)=(4x)/(y-1) ?

The solution for (dy)/(dx)=(4x)/(y-1) is y=1+sqrt(2(2x^2+c_{1))+1},y=1-sqrt(2(2x^2+c_{1))+1}

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(dy)/(dx)=(4x)/(y-1)

\frac{d y}{d x} = \frac{4 x}{y - 1}

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

Solution steps

\frac{d y}{d x} = \frac{4 x}{y - 1}

Solve separable ODE:

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

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

What is the solution for (dy)/(dx)=(4x)/(y-1) ?
The solution for (dy)/(dx)=(4x)/(y-1) is y=1+sqrt(2(2x^2+c_{1))+1},y=1-sqrt(2(2x^2+c_{1))+1}