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

The solution for sqrt(x-1)(dy)/(dx)= x/y ,y=1,x=2 is y=sqrt(4(((x-1)^{3/2))/3+sqrt(x-1))-13/3}

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sqrt(x-1)(dy)/(dx)= x/y ,y=1,x=2

x - 1 \frac{d y}{d x} = \frac{x}{y}, y = 1, x = 2

y = 4 (\frac{( x - 1 ) ^{\frac{3}{2}}}{3} + x - 1) - \frac{13}{3}

Solution steps

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

Solve separable ODE:

y = 4 (\frac{( x - 1 ) ^{\frac{3}{2}}}{3} + x - 1) - \frac{13}{3}

y = 4 (\frac{( x - 1 ) ^{\frac{3}{2}}}{3} + x - 1) - \frac{13}{3}

x y^{^{'}} + 2 y = y^{2}

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

y^{^{'}} = \frac{x + 1}{e ^{2 y}}

5 x cos (5 y) d y - sin (5 y) d x = 0

x y d x + 1 + x^{2} d y = 0

What is the solution for sqrt(x-1)(dy)/(dx)= x/y ,y=1,x=2 ?
The solution for sqrt(x-1)(dy)/(dx)= x/y ,y=1,x=2 is y=sqrt(4(((x-1)^{3/2))/3+sqrt(x-1))-13/3}