What is the solution for (2r-1)/t dr+(r-2r^2)/(t^2-1)dt=0 ?

The solution for (2r-1)/t dr+(r-2r^2)/(t^2-1)dt=0 is t=sqrt(c_{1)r^2+1},t=-sqrt(c_{1)r^2+1}

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(2r-1)/t dr+(r-2r^2)/(t^2-1)dt=0

\frac{2 r - 1}{t} d r + \frac{r - 2 r ^{2}}{t ^{2} - 1} d t = 0

t = c_{1} r^{2} + 1, t = - c_{1} r^{2} + 1

Solution steps

\frac{2 r - 1}{t} d r + \frac{r - 2 r ^{2}}{t ^{2} - 1} d t = 0

Solve separable ODE:

t = c_{1} r^{2} + 1, t = - c_{1} r^{2} + 1

t = c_{1} r^{2} + 1, t = - c_{1} r^{2} + 1

\frac{d}{d x} (3 x^{4} - 2 x^{3} - 12 x^{2} + 18 x + 15)

g (x) = x + x

2 sin (x), 3 cos (x)

\frac{d}{d x} (\frac{1}{ln ( x ^{2} )})

\frac{\partial}{\partial y} (x^{2} - y^{2})

What is the solution for (2r-1)/t dr+(r-2r^2)/(t^2-1)dt=0 ?
The solution for (2r-1)/t dr+(r-2r^2)/(t^2-1)dt=0 is t=sqrt(c_{1)r^2+1},t=-sqrt(c_{1)r^2+1}