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

The solution for (dy)/(dx)=(2x)/(1+2y),y(2)=1 is y=(-1+sqrt(4x^2-7))/2

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(dy)/(dx)=(2x)/(1+2y),y(2)=1

\frac{d y}{d x} = \frac{2 x}{1 + 2 y}, y (2) = 1

y = \frac{- 1 + 4 x ^{2} - 7}{2}

Solution steps

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

Solve separable ODE:

y = \frac{- 1 + 4 x ^{2} - 7}{2}

y = \frac{- 1 + 4 x ^{2} - 7}{2}

\frac{2 x}{y} d x - \frac{x ^{2}}{y ^{2}} d y = 0

f (x) = \frac{2 x}{7} + 1

\frac{d y}{d x} = (x - 2) e^{- 2 y}

\frac{\partial}{\partial x} ((2 - x) (5 - x - 2 y))

What is the solution for (dy)/(dx)=(2x)/(1+2y),y(2)=1 ?
The solution for (dy)/(dx)=(2x)/(1+2y),y(2)=1 is y=(-1+sqrt(4x^2-7))/2