What is the solution for (dy)/(dx)=(2y^2)/(sqrt(x)),y(9)= 1/49 ?

The solution for (dy)/(dx)=(2y^2)/(sqrt(x)),y(9)= 1/49 is y=-(4sqrt(x)+61)/(16x-3721)

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(dy)/(dx)=(2y^2)/(sqrt(x)),y(9)= 1/49

\frac{d y}{d x} = \frac{2 y ^{2}}{x}, y (9) = \frac{1}{49}

y = - \frac{4 x + 61}{16 x - 3721}

Solution steps

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

Solve separable ODE:

y = - \frac{4 x + 61}{16 x - 3721}

y = - \frac{4 x + 61}{16 x - 3721}

sin (2 x) d x + cos (3 y) d y = 0, y (\frac{π}{2}) = (\frac{π}{3})

\frac{d P}{d t} = 8 Pt, P (1) = 7

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

\frac{d}{d θ} (r (θ)) r (θ) = \frac{3}{17 - θ}

\frac{d x}{d t} = 75 - \frac{x}{100}, x = 4000, t = 0

What is the solution for (dy)/(dx)=(2y^2)/(sqrt(x)),y(9)= 1/49 ?
The solution for (dy)/(dx)=(2y^2)/(sqrt(x)),y(9)= 1/49 is y=-(4sqrt(x)+61)/(16x-3721)