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

The solution for x(dt)/(dx)=(a+at^2)/(1-at) is x=(e^{(arctan(t)+c_{1}a)/a})/(sqrt(t^2+1))

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x(dt)/(dx)=(a+at^2)/(1-at)

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

x = \frac{e ^{\frac{a r c t a n ( t ) + c _{1} a}{a}}}{t ^{2} + 1}

Solution steps

x \frac{d}{d x} (t) = \frac{a + a t ^{2}}{1 - a t}

Solve separable ODE:

x = \frac{e ^{\frac{a r c t a n ( t ) + c _{1} a}{a}}}{t ^{2} + 1}

x = \frac{e ^{\frac{a r c t a n ( t ) + c _{1} a}{a}}}{t ^{2} + 1}

sec (t) y^{^{'}} = - \frac{y ^{5}}{4}

y^{^{'}} = y (t + 1)

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

- y^{^{'}} = - 2 y

f (x) f^{^{'}} (x) = (x^{4} - 10)

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