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

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

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(dy)/(dx)=2xsqrt(y-1)

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

y = \frac{x ^{4} + c _{1}^{2}}{4} + \frac{c _{1} x ^{2}}{2} + 1

Solution steps

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

Solve separable ODE:

y = \frac{x ^{4} + c _{1}^{2}}{4} + \frac{c _{1} x ^{2}}{2} + 1

y = \frac{x ^{4} + c _{1}^{2}}{4} + \frac{c _{1} x ^{2}}{2} + 1

d y = e^{3 x - 2 y} d x

\frac{d y}{d x} = e^{3 x} e^{2 y}

y \frac{p d p}{d y} - (p)^{2} + p = 0

\frac{d y}{d x} = \frac{2 x + sec ^{2} ( x )}{2 y}, y (0) = - 2

y^{^{'}} = - 5 y e^{t}, y (0) = 1

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