What is the solution for (dx)/(dt)=(1-x^2)/(xt) ?

The solution for (dx)/(dt)=(1-x^2)/(xt) is x=(sqrt(-c_{1)+t^2})/t ,x=-(sqrt(-c_{1)+t^2})/t

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(dx)/(dt)=(1-x^2)/(xt)

\frac{d x}{d t} = \frac{1 - x ^{2}}{x t}

x = \frac{- c _{1} + t ^{2}}{t}, x = - \frac{- c _{1} + t ^{2}}{t}

Solution steps

\frac{d x}{d t} = \frac{1 - x ^{2}}{x t}

Solve separable ODE:

x = \frac{- c _{1} + t ^{2}}{t}, x = - \frac{- c _{1} + t ^{2}}{t}

x = \frac{- c _{1} + t ^{2}}{t}, x = - \frac{- c _{1} + t ^{2}}{t}

y^{^{'}} = \frac{x}{e ^{y}}

y^{^{'}} = \frac{x sin ( x )}{y}, y (0) = - 1

4 x y^{2} + (x^{2} + 1) y^{^{'}} = 0

d x = (8 x y + 3 y) d y

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

What is the solution for (dx)/(dt)=(1-x^2)/(xt) ?
The solution for (dx)/(dt)=(1-x^2)/(xt) is x=(sqrt(-c_{1)+t^2})/t ,x=-(sqrt(-c_{1)+t^2})/t