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

The solution for (dy)/(dx)=(sin^2(y))/(1-x^2) is y=arccot(-(ln(x+1)-ln(x-1)+c_{1})/2)+pin

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(dy)/(dx)=(sin^2(y))/(1-x^2)

\frac{d y}{d x} = \frac{sin ^{2} ( y )}{1 - x ^{2}}

y = arccot (- \frac{ln ( x + 1 ) - ln ( x - 1 ) + c _{1}}{2}) + πn

Solution steps

\frac{d y}{d x} = \frac{sin ^{2} ( y )}{1 - x ^{2}}

Solve separable ODE:

y = arccot (- \frac{ln ( x + 1 ) - ln ( x - 1 ) + c _{1}}{2}) + πn

y = arccot (- \frac{ln ( x + 1 ) - ln ( x - 1 ) + c _{1}}{2}) + πn

v^{2} x^{2} d x + x^{2} d x - 2 x^{2} v^{2} d x - 2 x^{3} v d v = 0

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

x^{^{'}} + 0.09 \cdot x = 0, x (0) = 1

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

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

What is the solution for (dy)/(dx)=(sin^2(y))/(1-x^2) ?
The solution for (dy)/(dx)=(sin^2(y))/(1-x^2) is y=arccot(-(ln(x+1)-ln(x-1)+c_{1})/2)+pin