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

The solution for (dy)/(dx)=2(1+x)(1+y^2) is y=tan(x^2+2x+c_{1})

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(dy)/(dx)=2(1+x)(1+y^2)

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

y = tan (x^{2} + 2 x + c_{1})

Solution steps

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

Solve separable ODE:

y = tan (x^{2} + 2 x + c_{1})

y = tan (x^{2} + 2 x + c_{1})

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

2 x y + 6 x + (x^{2} - 9) y^{^{'}} = 0

\frac{d y}{d x} - \frac{x}{2 y} = 0

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

x d y + y d x = 2 d x

What is the solution for (dy)/(dx)=2(1+x)(1+y^2) ?
The solution for (dy)/(dx)=2(1+x)(1+y^2) is y=tan(x^2+2x+c_{1})