What is the solution for 2r(s^2+1)dr+(r^4+1)ds=0 ?

The solution for 2r(s^2+1)dr+(r^4+1)ds=0 is s=tan(-arctan(r^2)+c_{1})

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2r(s^2+1)dr+(r^4+1)ds=0

2 r (s^{2} + 1) d r + (r^{4} + 1) d s = 0

s = tan (- arctan (r^{2}) + c_{1})

Solution steps

2 r (s^{2} + 1) d r + (r^{4} + 1) d s = 0

Solve separable ODE:

s = tan (- arctan (r^{2}) + c_{1})

s = tan (- arctan (r^{2}) + c_{1})

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x \to 1 lim (\frac{1}{x ^{2} - x})

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What is the solution for 2r(s^2+1)dr+(r^4+1)ds=0 ?
The solution for 2r(s^2+1)dr+(r^4+1)ds=0 is s=tan(-arctan(r^2)+c_{1})