What is the solution for (dy)/(dt)=1+t+y^2+ty^2 ?

The solution for (dy)/(dt)=1+t+y^2+ty^2 is y=tan((t^2)/2+t+c_{1})

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(dy)/(dt)=1+t+y^2+ty^2

\frac{d y}{d t} = 1 + t + y^{2} + t y^{2}

y = tan (\frac{t ^{2}}{2} + t + c_{1})

Solution steps

\frac{d y}{d t} = 1 + t + y^{2} + t y^{2}

Solve separable ODE:

y = tan (\frac{t ^{2}}{2} + t + c_{1})

y = tan (\frac{t ^{2}}{2} + t + c_{1})

2 y + 3 + (2 x - 4) \frac{d y}{d x} = 0

(x - 1) (\frac{d y}{d x}) = (4 - y^{2})

3 x y^{^{'}} - 2 y = 0, y (0) = x^{\frac{2}{3}}

cot (x) (e - y + 1) d x = (1 + sin^{2} (x)) d y

y^{^{'}} arctan (x) - y (1 + x^{2})^{- 1} = 0

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