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

The solution for (dy)/(dx)=(2+y^2)/(2xy),y(1)=1 is y=sqrt(3x-2)

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

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

y = 3 x - 2

Solution steps

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

Solve separable ODE:

y = 3 x - 2

y = 3 x - 2

\int x x^{2} + 3 d x

\int \frac{x}{- x ^{2} + 5} d x

\int_{0}^{\frac{3}{2}} x cos (π x) d x

- \frac{1}{2 x ^{2}}

x \to \infty lim (\frac{x ^{3} + 20 x}{10 x - 2})

What is the solution for (dy)/(dx)=(2+y^2)/(2xy),y(1)=1 ?
The solution for (dy)/(dx)=(2+y^2)/(2xy),y(1)=1 is y=sqrt(3x-2)